Linear colorings of subcubic graphs

Chun Hung Liu, Gexin Yu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induces a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and every assignment of lists of size four to the vertices of the graph, there exists a linear coloring such that the color of each vertex belongs to the list assigned to that vertex and the neighbors of every degree-two vertex receive different colors, unless the graph is C5 or K3,3. This confirms a conjecture raised by Esperet, Montassier and Raspaud [L.Esperet, M.Montassier, and A. Raspaud, Linear choosability of graphs, Discrete Math. 308 (2008) 3938-3950]. Our proof is constructive and yields a linear-time algorithm to find such a coloring.

Original languageEnglish (US)
Pages (from-to)1040-1050
Number of pages11
JournalEuropean Journal of Combinatorics
Issue number6
StatePublished - Aug 2013

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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