COMBINATORICS
2006
13 years 11 months ago
2006
We prove the following extension of an old result of Andr
EJC
2008
13 years 11 months ago
2008
The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex kcolouring of G in which the same colour never ...
EJC
2008
13 years 11 months ago
2008
Gerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience, 1995], page 115) conjectured that if a graph has no odd complete minor of order p, the...
DM
2008
13 years 11 months ago
2008
For graphs G and H, let G H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for GH. It is proved that (G H) max{ c(G)...
ENDM
2010
13 years 11 months ago
2010
A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Gr
DAM
2008
13 years 11 months ago
2008
This paper presents algorithms to find vertex-critical and edgecritical subgraphs in a given graph G, and demonstrates how these critical subgraphs can be used to determine the ch...
DM
2010
13 years 11 months ago
2010
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
CORR
2008
Springer
13 years 11 months ago
2008
Springer
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is th...
CORR
2010
Springer
13 years 11 months ago
2010
Springer
We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of fini...
SODA
2000
ACM
14 years 24 days ago
2000
ACM
We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...