242 research outputs found
On p-competition graphs of loopless Hamiltonian digraphs without symmetric arcs and graph operations
For a digraph , the -competition graph of is the graph satisfying the following: , for , if and only if there exist distinct vertices such that , for each .
We show the is a -competition graph of a loopless digraph without symmetric arcs for , where and are -competition graphs of loopless digraphs without symmetric arcs and . For -competition graphs of loopless Hamiltonian digraphs without symmetric arcs, we obtain similar results. And we show that a star is a -competition graph of a loopless Hamiltonian digraph without symmetric arcs if and .
Based on these results, we obtain conditions such that spiders, caterpillars and cacti are -competition graphs of loopless digraphs without symmetric arcs. We also obtain conditions such that these graphs are -competition graphs of loopless Hamiltonian digraphs without symmetric arcs
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Algorithmic Graph Theory
The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions
The competition hypergraphs of doubly partial orders
Since Cho and Kim (2005) showed that the competition graph of a doubly
partial order is an interval graph, it has been actively studied whether or not
the same phenomenon occurs for other variants of competition graph and
interesting results have been obtained. Continuing in the same spirit, we study
the competition hypergraph, an interesting variant of the competition graph, of
a doubly partial order. Though it turns out that the competition hypergraph of
a doubly partial order is not always interval, we completely characterize the
competition hypergraphs of doubly partial orders which are interval.Comment: 12 pages, 6 figure
d-반순서의 경쟁그래프의 연구
학위논문 (박사)-- 서울대학교 대학원 : 사범대학 수학교육과, 2018. 2. 김서령.The \emph{competition graph} of a digraph is defined to be a graph whose vertex set is the same as and which has an edge joining two distinct vertices and if and only if there are arcs and for some vertex in . Competition graphs have been extensively studied for more than four decades.
Cohen~\cite{cohen1968interval, cohen1977food, cohen1978food} empirically observed that most competition graphs of acyclic digraphs representing food webs are interval graphs. Roberts~\cite{roberts1978food} asked whether or not Cohen's observation was just an artifact of the construction, and then concluded that it was not by showing that if is an arbitrary graph, then together with additional isolated
vertices as many as the number of edges of is the competition graph of some acyclic digraph. Then he asked for a characterization of acyclic digraphs whose competition graphs are interval graphs. Since then, the problem has remained elusive and it has been one of the basic open problems in the study of competition graphs. There have been a lot of efforts to settle the problem and some progress has been made. While Cho and Kim~\cite{cho2005class} tried to answer his question, they could show that the competition graphs of doubly partial orders are interval graphs. They also showed that an interval graph together with sufficiently many isolated vertices is the competition graph of a doubly partial order.
In this thesis, we study the competition graphs of -partial orders some of which generalize the results on the competition graphs of doubly partial orders.
For a positive integer , a digraph is called a \emph{-partial order} if V(D) \subset \RR^d and there is an arc from a vertex to a vertex if and only if is componentwise greater than . A doubly partial order is a -partial order.
We show that every graph is the competition graph of a -partial order for some nonnegative integer , call the smallest such the \emph{partial order competition dimension} of , and denote it by .
This notion extends the statement that the competition graph of a doubly partial order is interval and the statement that any interval graph can be the competition graph of a doubly partial order as long as sufficiently many isolated vertices are added, which were proven by Cho and Kim~\cite{cho2005class}. Then we study the partial order competition dimensions of some interesting families of graphs. We also study the -step competition graphs and the competition hypergraph of -partial orders.1 Introduction 1
1.1 Basic notions in graph theory 1
1.2 Competition graphs 6
1.2.1 A brief history of competition graphs 6
1.2.2 Competition numbers 7
1.2.3 Interval competition graphs 10
1.3 Variants of competition graphs 14
1.3.1 m-step competition graphs 15
1.3.2 Competition hypergraphs 16
1.4 A preview of the thesis 18
2 On the competition graphs of d-partial orders 1 20
2.1 The notion of d-partial order 20
2.2 The competition graphs of d-partial orders 21
2.2.1 The regular (d − 1)-dimensional simplex △ d−1 (p) 22
2.2.2 A bijection from H d + to a set of regular (d − 1)-simplices 23
2.2.3 A characterization of the competition graphs of d-partial orders 25
2.2.4 Intersection graphs and competition graphs of d-partial orders 27
2.3 The partial order competition dimension of a graph 29
3 On the partial order competition dimensions of chordal graphs 2 38
3.1 Basic properties on the competition graphs of 3-partial orders 39
3.2 The partial order competition dimensions of diamond-free chordal graphs 42
3.3 Chordal graphs having partial order competition dimension greater than three 46
4 The partial order competition dimensions of bipartite graphs 3 53
4.1 Order types of two points in R 3 53
4.2 An upper bound for the the partial order competition dimension of a graph 57
4.3 Partial order competition dimensions of bipartite graphs 64
5 On the m-step competition graphs of d-partial orders 4 69
5.1 A characterization of the m-step competition graphs of dpartial orders 69
5.2 Partial order m-step competition dimensions of graphs 71
5.3 dim poc (Gm) in the aspect of dim poc (G) 76
5.4 Partial order competition exponents of graphs 79
6 On the competition hypergraphs of d-partial orders 5 81
6.1 A characterization of the competition hypergraphs of d-partial orders 81
6.2 The partial order competition hyper-dimension of a hypergraph 82
6.3 Interval competition hypergraphs 88
Abstract (in Korean) 99Docto
An Analysis of the Influence of Graph Theory When Preparing for Programming Contests
[EN] The subject known as Programming Contests in the Bachelor's Degree in Computer Engineering course focuses on solving programming problems frequently met within contests such as the Southwest Europe Regional Contest (SWERC). In order to solve these problems one first needs to model the problem correctly, find the ideal solution, and then be able to program it without making any mistakes in a very short period of time. Leading multinationals such as Google, Apple, IBM, Facebook and Microsoft place a very high value on these abilities when selecting candidates for posts in their companies. In this communication we present some preliminary results of an analysis of the interaction between two optional subjects in the Computer Science Degree course: Programming Contests (PC) and Graphs, Models and Applications (GMA). The results of this analysis enabled us to make changes to some of the contents in GMA in order to better prepare the students to deal with the challenges they have to face in programming contests.This project was funded by the Vicerrectorado de Estudios y Calidad Academica of the Universitat Politecnica de Valencia. PIME-B08: Modelos de la Teoria de Grafos aplicados a problemas de competiciones de programacion.Jordan-Lluch, C.; Gomez, J.; Conejero, JA. (2017). An Analysis of the Influence of Graph Theory When Preparing for Programming Contests. Mathematics. 5(1):1-11. doi:10.3390/math5010008S1115
Opinion Optimization in Directed Social Networks
Shifting social opinions has far-reaching implications in various aspects,
such as public health campaigns, product marketing, and political candidates.
In this paper, we study a problem of opinion optimization based on the popular
Friedkin-Johnsen (FJ) model for opinion dynamics in an unweighted directed
social network with nodes and edges. In the FJ model, the internal
opinion of every node lies in the closed interval , with 0 and 1 being
polar opposites of opinions about a certain issue. Concretely, we focus on the
problem of selecting a small number of nodes and changing their
internal opinions to 0, in order to minimize the average opinion at
equilibrium. We then design an algorithm that returns the optimal solution to
the problem in time. To speed up the computation, we further develop a
fast algorithm by sampling spanning forests, the time complexity of which is , with being the number of samplings. Finally, we execute extensive
experiments on various real directed networks, which show that the
effectiveness of our two algorithms is similar to each other, both of which
outperform several baseline strategies of node selection. Moreover, our fast
algorithm is more efficient than the first one, which is scalable to massive
graphs with more than twenty million nodes
Web browsing automation for applications quality control
Context: Quality control comprises the set of activities aimed to evaluate that software meets its specification and delivers the functionality expected by the consumers. These activities are often removed in the development process and, as a result, the final software product usually lacks quality. Objective: We propose a set of techniques to automate the quality control for web applications from the client-side, guiding the process by functional and nonfunctional requirements (performance, security, compatibility, usability and accessibility). Method: The first step to achieve automation is to define the structure of the web navigation. Existing software artifacts in the phase of analysis and design are reused. Then, the independent paths of navigation are found, and each path is traversed automatically using real browsers while different kinds of assessments are carried out. Results: The processes and methods proposed in this paper have been implemented by means of a reference architecture and open source tools. A laboratory experiment and an industrial case study have been performed in order to validate the proposal. Conclusion: The definition of navigation paths is a rich approach to model web applications. Grey-box (black-box and white-box) methods have been proved to be very valuable for web assessment. The Chinese Postman Problem (CPP) is an optimal way to find the independent paths in a web navigation modeled as a directed graph
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