Lih, Ko-Wei; Wang, Wei-Fan Coloring the square of an outerplanar graph. (English) Zbl 1135.05022 Taiwanese J. Math. 10, No. 4, 1015-1023 (2006). Summary: Let \(G\) be an outerplanar graph with maximum degree \(\Delta(G)\geq 3\). We prove that the chromatic number \(\chi(G^2)\) of the square of \(G\) is at most \(\Delta(G)+2\). This confirms a conjecture of G. Wegner [Graphs with given diameter and a coloring problem, preprint, University Dortmund (1977)] for outerplanar graphs. The upper bound can be further reduced to the optimal value \(\Delta(G)+1\) when \(\Delta(G)\geq 7\). Cited in 1 ReviewCited in 11 Documents MSC: 05C15 Coloring of graphs and hypergraphs PDFBibTeX XMLCite \textit{K.-W. Lih} and \textit{W.-F. Wang}, Taiwanese J. Math. 10, No. 4, 1015--1023 (2006; Zbl 1135.05022) Full Text: DOI