COMBINATORICS
2006
13 years 4 months ago
2006
We prove the following extension of an old result of Andr
EJC
2008
13 years 4 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 4 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 4 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 4 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 4 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 4 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 4 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 4 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
13 years 5 months 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 ...