Strong products of Kneser graphs
✍ Scribed by Sandi Klavžar; Uroš Milutinović
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 314 KB
- Volume
- 133
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Let G [XI H be the strong product of graphs G and H. We give a short proof that
Kneser graphs are then used to demonstrate that this lower bound is sharp. We also prove that for every n > 2 there is an infinite sequence of pairs of graphs G and G' such that G' is not a retract of G while G' IXI K, is a retract of G ixI K..
📜 SIMILAR VOLUMES
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## Abstract The vertex set of the reduced Kneser graph KG~2~(__m,2__) consists of all pairs {__a,b__} such that __a, b__ε{1,2,…,__m__} and 2≤|__a__−__b__|≤__m__−2. Two vertices are defined to be adjacent if they are disjoint. We prove that, if __m__≥4 __and m__≠5, then the circular chromatic number
Let X ϭ ͕ 1 , 2 , . . . , n ͖ be a set of n elements and let X ( r ) be the collection of all the subsets of X containing precisely r elements . Then the generalised Kneser graph K ( n , r , s ) (when 2 r Ϫ s р n ) is the graph with vertex set X ( r ) and edges AB for A , B X ( r ) with ͉ A ʝ B ͉ р