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Note on incidence chromatic number of subquartic graphs

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Abstract

An incidence in a graph G is a pair (ve) where v is a vertex of G and e is an edge of G incident to v. Two incidences (ve) and (uf) are adjacent if at least one of the following holds: \((a) v = u, (b) e = f\), or \((c) vu \in \{e,f\}\). An incidence coloring of G is a coloring of its incidences assigning distinct colors to adjacent incidences. In this note we prove that every subquartic graph admits an incidence coloring with at most seven colors.

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Acknowledgments

The authors are thankful to the two anonymous referees for their comments that helped improve the presentation of the proof. This research was supported by the Czech Science Foundation Grant GA14–10799S, Slovak VEGA Grant no. 1 / 0368 / 16, and Slovenian Research Agency Program P1–0383. The second author also acknowledges partial support by the National Scholarship Programme of the Slovak Republic.

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Correspondence to Borut Lužar.

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Gregor, P., Lužar, B. & Soták, R. Note on incidence chromatic number of subquartic graphs. J Comb Optim 34, 174–181 (2017) doi:10.1007/s10878-016-0072-2

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Keywords

  • Incidence coloring
  • Subquartic graph
  • Incidence chromatic number