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List Homomorphisms and Circular Arc Graphs

✍ Scribed by Tomas Feder; Pavol Hell; Jing Huang


Book ID
106167951
Publisher
Springer-Verlag
Year
1999
Tongue
English
Weight
326 KB
Volume
19
Category
Article
ISSN
0209-9683

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## Abstract Given graphs __G__, __H__, and lists __L__(__v__) βŠ† __V__(__H__), __v__ Ξ΅ __V__(__G__), a list homomorphism of __G__ to __H__ with respect to the lists __L__ is a mapping __f__ : __V__(__G__) β†’ __V__(__H__) such that __u__v Ξ΅ __E__(__G__) implies __f__(__u__)__f__(__v__) Ξ΅ __E__(__H__),

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Let H be a fixed graph. We introduce the following list homomorphism problem: Given an input graph G and for each vertex v of G a ``list'' L(v) V(H), decide whether or not there is a homomorphism f : We discuss this problem primarily in the context of reflexive graphs, i.e., graphs in which each ve

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## Abstract We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two, which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that w

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## Abstract A graph with __n__ vertices that contains no triangle and no 5‐cycle and minimum degree exceeding __n__/4 contains an independent set with at least (3__n__)/7 vertices. This is best possible. The proof proceeds by producing a homomorphism to the 7‐cycle and invoking the No Homomorphism