Abu-Khzam, Faisal N. and Langston, Michael A. - Immersion containment and connectivity in color-critical graphs

dmtcs:589 - Discrete Mathematics & Theoretical Computer Science, October 30, 2012, Vol. 14 no. 2
Immersion containment and connectivity in color-critical graphs

Authors: Abu-Khzam, Faisal N. and Langston, Michael A.

The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. It is shown that a t-chromatic graph G contains either an immersed Kt or an immersed t-chromatic subgraph that is both 4-vertex-connected and t-edge-connected. This gives supporting evidence of our conjecture that if G requires at least t colors, then Kt is immersed in G.


Source : oai:HAL:hal-00990594v1
Volume: Vol. 14 no. 2
Section: Graph Theory
Published on: October 30, 2012
Submitted on: January 10, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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