Immersion Containment and Connectivity in Color-Critical Graphs
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-...
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| Format: | article |
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2012
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| Online Access: | http://hdl.handle.net/10725/2774 http://dmtcs.episciences.org/589 |
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| Summary: | 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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