✦ LIBER ✦

Intersection properties of graphs

✍ Scribed by Terry A. McKee

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 550 KB
Volume: 89
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90118-l

No coin nor oath required. For personal study only.

✦ Synopsis

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 simple formal language, based on vertices and paths, which supports transfer of selected information about the original property to its intersection property. For instance, a simple description of paths produces the asteroidal triple characterization of interval graphs.

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## Abstract The intersection dimension of a bipartite graph with respect to a type __L__ is the smallest number __t__ for which it is possible to assign sets __A__~__x__~⊆{1, …, __t__} of labels to vertices __x__ so that any two vertices __x__ and __y__ from different parts are adjacent if and only