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Immersion containment and connectivity in color-critical graphs

Abstract : 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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Faisal N. Abu-Khzam, Michael A. Langston. Immersion containment and connectivity in color-critical graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.155--164. ⟨hal-00990594⟩

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