Discrete Mathematics & Theoretical Computer Science, Vol 14, No 2 (2012)

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Immersion Containment and Connectivity in Color-Critical Graphs

Faisal N. Abu-Khzam, Michael A. Langston


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.

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