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Intersection theory for graphs

✍ Scribed by Tom Brylawski


Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
657 KB
Volume
30
Category
Article
ISSN
0095-8956

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It is known that for a graph on \(n\) vertices \(\left\lfloor n^{2} / 4\right\rfloor+1\) edges is sufficient for the existence of many triangles. In this paper, we determine the minimum number of edges sufficient for the existence of \(k\) triangles intersecting in exactly one common vertex. C 1995

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McKee, T.A., Intersection properties of graphs, Discrete Mathematics 89 (1991) 253-260. For each graph-theoretic property, we define a corresponding 'intersection property', motivated by the natural relationship of paths with interval graphs, and of trees with chordal graphs. We then develop a simp

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Hartman I.B.-A., I. Newman and R. Ziv, On grid intersection graphs, Discrete Mathematics 87 (1991) 41-52. A bipartite graph G = (X, Y; E) has a grid representation if X and Y correspond to sets of horizontal and vertical segments in the plane, respectively, such that (xi, y,) E E if and only if segm

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Two variations of set intersection representation are investigated and upper and lower bounds on the minimum number of labels with which a graph may be represented are found that hold for almost all graphs. Specifically, if &(G) is defined to be the minimum number of labels with which G may be repre

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✍ BΓ©la BollobΓ‘s; Alex Scott πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 193 KB

Let G and H be two graphs of order n. If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this article is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of Erd" os,