97
Voted
DM
2008
14 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...
81
Voted
DM
2002
15 years 2 days 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
15 years 2 days 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
15 years 3 days 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 ...
93
Voted
ARSCOM
2005
15 years 5 days 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...
98
Voted
MST
2008
15 years 6 days 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...
87
Voted
EJC
2007
15 years 6 days 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...
106
Voted
WG
2005
Springer
15 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 ...