The solution of two problems on bound polysemy

A pair of graphs ( G 1, G 2) on the same set of vertices V is called bound polysemic, if there is a poset P=( V,⩽) such that for all u, v∈ V with u≠ v, uv is an edge of G 1 if and only if there is some w∈ V such that u⩽ w and v⩽ w and uv is an edge of G 2 if and only if there is some w∈ V such that...

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Published inDiscrete mathematics Vol. 282; no. 1; pp. 257 - 261
Main Authors Fischermann, Miranca, Knoben, Werner, Kremer, Dirk, Rautenbach, Dieter
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 06.05.2004
Elsevier
Subjects
Algebra
Bound graph
Clique
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
Polysemic pair
Polysemy
Poset
Sciences and techniques of general use
Poset
Clique
Bound graph
Polysemic pair
Polysemy
Partially ordered set
Discrete mathematics
Problem solving
Graph theory
Algorithm
Bounded solution
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Summary:A pair of graphs ( G 1, G 2) on the same set of vertices V is called bound polysemic, if there is a poset P=( V,⩽) such that for all u, v∈ V with u≠ v, uv is an edge of G 1 if and only if there is some w∈ V such that u⩽ w and v⩽ w and uv is an edge of G 2 if and only if there is some w∈ V such that w⩽ u and w⩽ v. Solving two problems posed by Tanenbaum (Electron. J. Comb. 7 (2000) R43), we characterize the bound polysemic pairs for which the poset P is unique and we describe an algorithm to recognize bound polysemic pairs in O(|V| 3) time.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2003.12.010