Sidorenko's Conjecture, Colorings and Independent Sets
نویسندگان
چکیده
منابع مشابه
Sidorenko's Conjecture, Colorings and Independent Sets
Let hom(H,G) denote the number of homomorphisms from a graph H to a graph G. Sidorenko’s conjecture asserts that for any bipartite graph H, and a graph G we have hom(H,G) > v(G) ( hom(K2, G) v(G)2 )e(H) , where v(H), v(G) and e(H), e(G) denote the number of vertices and edges of the graph H and G, respectively. In this paper we prove Sidorenko’s conjecture for certain special graphs G: for the ...
متن کاملExtracting List Colorings from Large Independent Sets
We take an application of the Kernel Lemma by Kostochka and Yancey [10] to its logical conclusion. The consequence is a sort of magical way to draw conclusions about list coloring (and online list coloring) just from the existence of an independent set incident to many edges. We use this to prove an Ore-degree version of Brooks’ Theorem for online list-coloring. The Ore-degree of an edge xy in ...
متن کاملA conjecture on independent sets and graph covers
In this article, I present a simple conjecture on the number of independent sets on graph covers. The conjecture implies that the partition function of a binary pairwise attractive model is greater than that of the Bethe approximation.
متن کامل?-Independent and Dissociate Sets on Compact Commutative Strong Hypergroups
In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...
متن کاملA relaxed Hadwiger's Conjecture for list colorings
Hadwiger’s Conjecture claims that any graph without Kk as a minor is (k − 1)-colorable. It has been proved for k ≤ 6, and is still open for every k ≥ 7. It is not even known if there exists an absolute constant c such that any ck-chromatic graph has Kk as a minor. Motivated by this problem, we show that there exists a computable constant f(k) such that any graph G without Kk as a minor admits a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6019