Independent sets of maximal size in tensor powers of vertex-transitive graphs
نویسندگان
چکیده
Let G be a connected, non-bipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G×G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif [8].
منابع مشابه
Stable sets of maximal size in Kneser-type graphs
We introduce a family of vertex-transitive graphs with specified subgroups of automorphisms which generalise Kneser graphs, powers of complete graphs and Cayley graphs of permutations. We compute the stability ratio for a wide class of these. Under certain conditions we characterise their stable sets of maximal size. © 2003 Elsevier Ltd. All rights reserved. MSC (2000): 05D05; 05C99
متن کاملIndependent sets in direct products of vertex-transitive graphs
Let G and H be two vertex-transitive graphs. It is easy to find that α(G × H) = |G||H | 2 if one of them is a bipartite graph. In this paper, we will identify the structure of the maximal-sized independent sets in G×H when one of them is a bipartite graph.
متن کاملVertex-transitive CIS graphs
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...
متن کاملIndependent sets in tensor graph powers
The tensor product of two graphs, G and H, has a vertex set V (G) × V (H) and an edge between (u, v) and (u′, v′) iff both uu′ ∈ E(G) and vv′ ∈ E(H). Let A(G) denote the limit of the independence ratios of tensor powers of G, limα(G)/|V (G)|. This parameter was introduced in [5], where it was shown that A(G) is lower bounded by the vertex expansion ratio of independent sets of G. In this note w...
متن کاملTwo-geodesic transitive graphs of prime power order
In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Graph Theory
دوره 60 شماره
صفحات -
تاریخ انتشار 2009