Immersion containment and connectivity in color-critical graphs
Faisal N. Abu-Khzam, Michael Allen Langston · Discrete Mathematics & Theoretical Computer Science · 2012
Graph Theory 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.