Faisal N. Abu-Khzam ; Michael A. Langston - Immersion containment and connectivity in color-critical graphs

dmtcs:589 - Discrete Mathematics & Theoretical Computer Science, October 30, 2012, Vol. 14 no. 2 - https://doi.org/10.46298/dmtcs.589
Immersion containment and connectivity in color-critical graphs

Authors: Faisal N. Abu-Khzam 1; Michael A. Langston 2

  • 1 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.


Volume: Vol. 14 no. 2
Section: Graph Theory
Published on: October 30, 2012
Accepted on: June 9, 2015
Submitted on: January 10, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Research Infrastructure: The Scalable Intracampus Research Grid for Computer Science Research; Funder: National Science Foundation; Code: 9972889
  • Towards an Automated Development Environment for Parallel Computing with Reconfigurable Processing Elements; Funder: National Science Foundation; Code: 0075792

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo DOI 10.1016/0012-365x(74)90045-4
  • 10.1016/0012-365x(74)90045-4
On critical subgraphs of colour-critical graphs

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