We study the generating functions for the number of stable sets of all cardinalities, in the case of graphs which are Cartesian products by paths, cycles, or trees. Explicit results are given for products by cliques. Algorithms based on matrix products are derived for grids, cylinders, toruses and h
Counting representable sets on simple graphs
β Scribed by Peter G. Jeavons
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 745 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0166-218X
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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__~β{1, β¦, __t__} of labels to vertices __x__ so that any two vertices __x__ and __y__ from different parts are adjacent if and only
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
PrCa, P., Graphs and topologies on discrete sets, Discrete Mathematics 103 (1992) 189-197. We show that a graph admits a topology on its node set which is compatible with the usual connectivity of undirected graphs if, and only if, it is a comparability graph. Then, we give a similar condition for