Near-interval edge colorings of graphs
Year: 2025
Type: article
Abstract: An interval edge coloring of a graph is a proper edge coloring by integers such that the colors on the edges incident with any vertex form an interval of integers. Not all graphs are interval colorable; a simple counterexample is K 3 . A near-interval coloring is a proper edge coloring of a graph such that the colors on the edges incident with any vertex is either an interval or a near-interval , where the latter is an interval except for one missing integer. We prove that all graphs of maximum degree at most 4, and all Class 1 graphs of maximum degree 5 and no vertices of degree 3 are near-interval colorable, thereby improving previous results by Petrosyan et al. (2010). We also consider the problem of near-interval coloring outerplanar graphs. For bipartite graphs , we prove that every such multigraph of maximum degree at most 5 admits a near-interval coloring, and that for every Δ ≥ 18 there is a bipartite graph of maximum degree Δ with no near-interval coloring. For the case of bipartite multigraphs, we give analogous examples of graphs of maximum degrees Δ with no near-interval coloring for every Δ ≥ 15 . Finally, we present classes of bipartite multigraphs of maximum degree 6,7 and 8 that admit near-interval colorings.
Source: Discrete Applied Mathematics
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4409260361