Department

Mathematics

Document Type

Article

Publication Date

7-2017

Embargo Period

8-31-2017

Abstract

Let c : E(G) → [k] be an edge-coloring of a graph G, not necessarily proper. For each vertex v, let c¯(v) = (a1, . . . , ak), where ai is the number of edges incident to v with color i. Reorder ¯c(v) for every v in G in nonincreasing order to obtain c ∗ (v), the color-blind partition of v. When c ∗ induces a proper vertex coloring, that is, c ∗ (u) 6= c ∗ (v) for every edge uv in G, we say that c is color-blind distinguishing. The minimum k for which there exists a color-blind distinguishing edge coloring c : E(G) → [k] is the colorblind index of G, denoted dal(G). We demonstrate that determining the color-blind index is more subtle than previously thought. In particular, determining if dal(G) ≤ 2 is NP-complete. We also connect the color-blind index of a regular bipartite graph to 2-colorable regular hypergraphs and characterize when dal(G) is finite for a class of 3-regular graphs.

Journal

Discrete Applied Mathematics

Journal ISSN

0166-218X

Volume

225

First Page

122

Last Page

129

Digital Object Identifier (DOI)

10.1016/j.dam.2017.03.006

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