Some results on the injective chromatic number of graphs

Min Chen, Geňa Hahn, André Raspaud and Weifan Wang ()
Additional contact information
Min Chen: Zhejiang Normal University
Geňa Hahn: Université de Montréal
André Raspaud: Université Bordeaux I
Weifan Wang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 3, No 10, 299-318

Abstract: Abstract A k-coloring of a graph G=(V,E) is a mapping c:V→{1,2,…,k}. The coloring c is injective if, for every vertex v∈V, all the neighbors of v are assigned with distinct colors. The injective chromatic number χ i (G) of G is the smallest k such that G has an injective k-coloring. In this paper, we prove that every K 4-minor free graph G with maximum degree Δ≥1 has $\chi_{i}(G)\le \lceil \frac{3}{2}\Delta\rceil$ . Moreover, some related results and open problems are given.

Keywords: Injective coloring; K 4-minor free graph; Planar graph; Maximum degree (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10878-011-9386-2

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