Immersion containment and connectivity in color-critical graphs

Faisal N. Abu-Khzam (1) , Michael A. Langston (2)

1 CSM/SAS/LAU - Department of Computer Science and Mathematics [Lebanese American University]
2 Department of Electrical Engineering and Computer Science [Knoxville]

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.

Domaines: Mathématique discrète [cs.DM]

Faisal N. Abu-Khzam, Michael A. Langston. Immersion containment and connectivity in color-critical graphs. Discrete Mathematics and Theoretical Computer Science, 2012, Vol. 14 no. 2 (2), pp.155--164. ⟨10.46298/dmtcs.589⟩. ⟨hal-00990594⟩