Paths And Cycles In Directed Graphs
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Paths And Cycles In Directed Graphs
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Author : Zvi Gregory Gutin
language : en
Publisher:
Release Date : 1993
Paths And Cycles In Directed Graphs written by Zvi Gregory Gutin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Paths Cycles And Related Partitioning Problems In Graphs
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Author : Zanbo Zhang
language : en
Publisher:
Release Date : 2017
Paths Cycles And Related Partitioning Problems In Graphs written by Zanbo Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
In this thesis we contribute with new theoretical results and algorithms to the research area related to cycles and paths in (directed) graphs. In Chapter 2, we improve a classical result of Woodall for Hamiltonicity in digraphs, involving the sum of the in-degree and out-degree of two vertices for which there is no arc from one to another, by characterizing the exceptional digraphs for the weakened condition.In Chapter 3, we introduce and study the concept of path extendability in digraphs. Several degree and extremal conditions for path extendability are presented, and path extendability of regular tournaments is settled. Some open problems are raised.In Chapter 4, we study cycle extendability in bipartite tournaments. We prove that in bipartite tournaments, Hamiltonicity, pancyclicity and cycle extendability are equivalent properties, with only one exceptional class that can be clearly described. We propose problems for further consideration involving the equivalence of these properties in the more general class of multipartite tournaments. In Chapter 5, we calculate the number of 2-paths between every vertex pair, a concept that one often encounters in conditions for cycle and path properties, in random oriented graphs and random tournaments. Based on our enumeration, we obtain several results related to path extendability in tournaments.In Chapter 6, we study computational problems in the context of cycle partitions and clique partitions of edge-colored graphs, which can be viewed as a generalization of digraphs. The results of this chapter deal with computational complexity and algorithmic aspects.Some new methods and tools are developed. In Chapter 5, the number of 2-paths is used in conditions or as a tool for establishing properties related to cycles and paths in tournaments. In Chapter 4, we define the concept of the in-out graph of a digraph, which is used to construct and analyze the structure of cycle factors of two intersecting cycles. To establish a degree condition for path extendability in Chapter 3, we introduce a contraction operation to relate path-extendability and cycle-extendability, so that we can use a former result of Hendry to simplify one of our proofs.
Digraphs
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Author : Jorgen Bang-Jensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Digraphs written by Jorgen Bang-Jensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.
Encyclopedia Of Algorithms
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Author : Ming-Yang Kao
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-06
Encyclopedia Of Algorithms written by Ming-Yang Kao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Computers categories.
One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.
Cycles And Rays
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cycles And Rays written by Gena Hahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.
Analysis And Enumeration
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Author : Andrea Marino
language : en
Publisher: Springer
Release Date : 2015-03-23
Analysis And Enumeration written by Andrea Marino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-23 with Computers categories.
In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions, that can be solved by using a non trivial brute-force approach. Given a metabolic network, each individual story should explain how some interesting metabolites are derived from some others through a chain of reactions, by keeping all alternative pathways between sources and targets. Enumerating cycles or paths in an undirected graph, such as a protein-protein interaction undirected network, is an example of an enumeration problem in which all the solutions can be listed through an optimal algorithm, i.e. the time required to list all the solutions is dominated by the time to read the graph plus the time required to print all of them. By extending this result to directed graphs, it would be possible to deal more efficiently with feedback loops and signed paths analysis in signed or interaction directed graphs, such as gene regulatory networks. Finally, enumerating mouths or bubbles with a source s in a directed graph, that is enumerating all the two vertex-disjoint directed paths between the source s and all the possible targets, is an example of an enumeration problem in which all the solutions can be listed through a linear delay algorithm, meaning that the delay between any two consecutive solutions is linear, by turning the problem into a constrained cycle enumeration problem. Such patterns, in a de Bruijn graph representation of the reads obtained by sequencing, are related to polymorphisms in DNA- or RNA-seq data.
Finding Patterns Short Cycles And Long Shortest Paths In Graphs
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Author : Mina Dalirrooyfard
language : en
Publisher:
Release Date : 2022
Finding Patterns Short Cycles And Long Shortest Paths In Graphs written by Mina Dalirrooyfard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This thesis is about finding useful structures in a graph using fast algorithms, or showing that no such fast algorithms exist using popular fine-grained hypotheses from the field of Fine-Grained Complexity. These structures can be any small fixed-sized pattern, or more specific bigger structures such as the longest shortest path in a graph, the size of which is represented by the diameter of a graph. Finding these structures has many applications, from protein-protein interactions in biology to anomaly detection in networks. We start by the problem of finding fixed-sized patterns in graphs as a subgraph, known as Graph Pattern Detection or Subgraph Isomorphism. There are no fast algorithms for graph pattern detection for many patterns despite many efforts, and so we focus on finding the source of hardness of detecting different patterns. One of our results is that one such source is the appearance of cliques (complete graphs) in the pattern which can make the pattern hard to detect. We then move to patterns that are not necessarily fixed sized but are either paths or cycles. The size of these patterns are often represented by popular parameters such as the diameter, radius and girth in the graph. We focus on computing the diameter (longest shortest path) of a graph and more specifically on approximating the diameter since computing it exactly is known to be hard. There is a folklore 2-approximation algorithm for the diameter that works in linear time, and we show that this algorithm is optimal conditioned on the Strong Exponential Time Hypothesis (SETH). Our result shows that any better than 2-approximation algorithm for the diameter requires super linear time. Moreover, we give a series of time-accuracy trade-off lower bounds, completing a line of recent works. The next pattern we discuss is a cycle, and more specifically it is the shortest cycle of a graph, the length of which is known to be the girth. We give the first 2-approximation algorithm for computing the girth in directed graphs in subquadratic time, improving the previous best approximation factor (in subquadratic time) which was 3. Finally, we don't resort to the standard measures of these distance problems, as in many applications we need more specific notions of these problems. For example we might be only interested in the longest shortest path among specific pairs of vertices (a variant of the diameter). Hence we consider two variants: First we assume that we are given two subsets S and T of the vertex set of the graph, and we are asked to compute distance parameters such as diameter and radius by only considering the pairs of nodes in S × T. These problems are called ST-distance problems and when S and T are non-overlapping and cover all the vertex set, they are called bichromatic distance problems. We give a comprehensive study of approximation of ST and bichromatic distance parameters. "Second, we consider a "symmetric" distance measure in directed graphs called min-distance. We give big improvements in approximating min-diameter and min-radius in general graphs and in directed acyclic graphs.
Paths And Cycles In Digraphs
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Author : Saddam Zaid
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-08
Paths And Cycles In Digraphs written by Saddam Zaid and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08 with categories.
This book is intended to investigate a famous conjecture in Graph Theory proposed by Caccetta and Haggkvist in 1978. The book demonstrates the conjecture which has two forms, and the equivalence of the two forms of the conjecture is proven. The conjecture relates the outdegree of the vertices in a digraph along with the existence of a short directed cycle of certain length in that digraph. Here, two main approaches to resolve the conjecture will be described. The first approach is by Hamidoune to prove the conjecture if the outdegree of each vertex in the digraph is at most three. The second approach is by Hoang and Reed to prove the conjecture if the outdegree of each vertex in the digraph is at most five. Both these approaches are investigated in detail and new techniques are developed in order to be used for subsequent research. Occasionally, the techniques used to prove the conjecture if the outdegree of each vertex is five can also be used to prove the conjecture if the outdegree of each vertex is six.
Theory And Application Of Graphs
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Author : Junming Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-31
Theory And Application Of Graphs written by Junming Xu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Mathematics categories.
In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. This book provides an introduction to graph theory for these students. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject.
Applications Of Graph Theory Algorithms
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Author : Vinod Chachra
language : en
Publisher: North Holland
Release Date : 1979
Applications Of Graph Theory Algorithms written by Vinod Chachra and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Basic concepts. Historical. Graphs. Vertices. Edges, edge sequences, and connectedness. Planar and nonplanar graphs. Separable and nonseparable graphs. Directed graphs. Algorithms for paths and trees. Network flows and graph traversing. Flows and potentials. Flows and capacity constraints. The transportation problem. Feasible and maximal flows. Algorithms for circuits and flow. Activity schedules. Construction. Sequencing and line balancing. Facilities design. Electrical energy. Pipeline flows, transportation and traffic. Production planning and control. Organization.