DM
2008
13 years 10 months ago
2008
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying pS(x + y) = TU=S pT (x)pU (y). Using umbral calculus, we give a formula for t...
DM
2002
13 years 11 months ago
2002
For a graph G, let P(G; ) be its chromatic polynomial and let [G] be the set of graphs having P(G; ) as their chromatic polynomial. We call [G] the chromatic equivalence class of ...
DM
2002
13 years 11 months ago
2002
It is known that the chromatic polynomial of any chordal graph has only integer roots. However, there also exist non-chordal graphs whose chromatic polynomials have only integer r...
CPC
2004
13 years 11 months ago
2004
This note presents two results on real zeros of chromatic polynomials. The first result states that if G is a graph containing a q-tree as a spanning subgraph, then the chromatic ...
ARSCOM
2005
13 years 11 months ago
2005
A class of graphs called generalized ladder graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven. In addition a formula for...
MST
2008
13 years 11 months ago
2008
Abstract. We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generaliz...
EJC
2007
13 years 11 months ago
2007
Given a graph we show how to construct a family of manifolds whose Euler characteristics are the values of the chromatic polynomial of the graph at various integers. The manifolds...
WG
2005
Springer
14 years 5 months ago
2005
Springer
In this paper, we present a new algorithm for computing the chromatic polynomial of a general graph G. Our method is based on the addition of edges and contraction of non-edges of ...