Graph coloring and the immersion order

Authors:
Faisal N. Abu-Khzam;Michael A. Langston
Affiliations:
Department of Computer Science, University of Tennessee, Knoxville, TN;Department of Computer Science, University of Tennessee, Knoxville, TN
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

Citing 9
Cited 1

Nonconstructive tools for proving polynomial-time decidability

Journal of the ACM (JACM)
On well-partial-order theory and its application to combinatorial problems of VLSI design

SIAM Journal on Discrete Mathematics
Regular Article: On search, decision, and the efficiency of polynomial-time algorithms

Proceedings of the 30th IEEE symposium on Foundations of computer science
Colouring, stable sets and perfect graphs

Handbook of combinatorics (vol. 1)
On algorithmic applications of the immersion order

Discrete Mathematics - Special issue on Graph theory
Fast algorithms for K4 immersion testing

Journal of Algorithms
Extremal Graph Theory

Extremal Graph Theory
Any 7-Chromatic Graphs Has K 7 Or K 4,4 As A Minor

Combinatorica
On the connectivity of minimum and minimal counterexamples to Hadwiger's Conjecture

Journal of Combinatorial Theory Series B

Characterizing graphs of small carving-width

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. These lead to the conjecture that, if G requires at least t colors, then G must have immersed within it Kt, the complete graph on t vertices. Evidence in support of such a proposition is presented. For each fixed value of t, there can be only a finite number of minimal counterexamples. These counterexamples are characterized based on Kempe chains, connectivity, cutsets and degree bounds. It is proved that minimal counterexamples must, if any exist, be both 4-vertex-connected and t-edge-connected.