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On Group Choosability of Total Graphs

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Abstract

In this paper, we study the group and list group colorings of total graphs and present group coloring versions of the total and list total colorings conjectures. We establish the group coloring version of the total coloring conjecture for the following classes of graphs: graphs with small maximum degree, two-degenerate graphs, planner graphs with maximum degree at least 11, planner graphs without certain small cycles, outerplanar graphs and near outerplanar graphs with maximum degree at least 4. In addition, the group version of the list total coloring conjecture is established for forests, outerplanar graphs and graphs with maximum degree at most two.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China

    H. J. Lai

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26505, USA

    H. J. Lai

  3. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    G. R. Omidi & G. Raeisi

  4. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    G. R. Omidi

Authors
  1. H. J. Lai
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  2. G. R. Omidi
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  3. G. Raeisi
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Correspondence to H. J. Lai.

Additional information

G. R. Omidi’s research was in part supported by a Grant from IPM (No.89050037).

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Lai, H.J., Omidi, G.R. & Raeisi, G. On Group Choosability of Total Graphs. Graphs and Combinatorics 29, 585–597 (2013). https://doi.org/10.1007/s00373-011-1114-2

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  • DOI: https://doi.org/10.1007/s00373-011-1114-2

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