منابع مشابه
Counting Colorings of a Regular Graph
At most how many (proper) q-colorings does a regular graph admit? Galvin and Tetali conjectured that among all n-vertex, d-regular graphs with 2d|n, none admits more q-colorings than the disjoint union of n/2d copies of the complete bipartite graph Kd,d. In this note we give asymptotic evidence for this conjecture, showing that the number of proper q-colorings admitted by an n-vertex, d-regular...
متن کاملMaximizing H-Colorings of a Regular Graph
For graphs G and H, a homomorphism from G to H, or H-coloring of G, is an adjacency preserving map from the vertex set of G to the vertex set of H. Our concern in this paper is the maximum number of H-colorings admitted by an n-vertex, d-regular graph, for each H. Specifically, writing hom(G,H) for the number of H-colorings admitted by G, we conjecture that for any simple finite graph H (perhap...
متن کاملOn Counting Generalized Colorings
The notion of graph polynomials definable in Monadic Second Order Logic, MSOL, was introduced in [Mak04]. It was shown that the Tutte polynomial and its generalization, as well as the matching polynomial, the cover polynomial and the various interlace polynomials fall into this category. In this paper we present a framework of graph polynomials based on counting functions of generalized colorin...
متن کاملCounting the number of non-equivalent vertex colorings of a graph
We study the number P(G) of non-equivalent ways of coloring a given graph G. We show some similarities and differences between this graph invariant and the well known chromatic polynomial. Relations with Stirling numbers of the second kind and with Bell numbers are also given. We then determine the value of this invariant for some classes of graphs. We finally study upper and lower bounds on P(...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2014
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-013-1403-z