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COMBINATORICS

2006

10 years 1 months ago
2006

We prove the following extension of an old result of Andr

EJC

2008

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 2 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 ...