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Note on the perfect EIC-graphs
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DOI：10.1016/j.amc.2016.05.031.png)
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Abstract
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Three edges e(1), e(2) and e(3) in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The injective edge coloring number chi(i)' (G) is the minimum number of colors permitted in a coloring of the edges of G such that if e(1), e(2) and e(3) are consecutive edges in G, then e(1) and e(3) receive the different colors. Let omega' denote the number of edges in a maximum clique of G. A graph G is called an omega' edge injective colorable (or perfect EIC-) graph if chi(i)' (G) = omega'. In this paper, we give a sharp bound of the injective coloring number of a 2-connected graph with some forbidden conditions, and then we also characterize some perfect EIC-graph classes, which extends the results of perfect EIC-graph of Cardoso et al. in [Injective edge chromatic index of a graph, http://arxiv.org/abs/1510.02626.]. (C) 2016 Elsevier Inc. All rights reserved.
Keywords:
Edge coloring
Injective coloring
Injective edge coloring
Injective edge chromatic index
Perfect EIC-graph
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