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Facial rainbow edge-coloring of simple 3-connected plane graphs

2020
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Opuscula Mathematica
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A facial rainbow edge-coloring of a plane graph \(G\) is an edge-coloring such that any two edges receive distinct colors if they lie on a common facial path of \(G\). The minimum number of colors used in such a coloring is denoted by \(\text{erb}(G)\). Trivially, \(\text{erb}(G) \geq \text{L}(G)+1\) holds for every plane graph without cut-vertices, where \(\text{L}(G)\) denotes the length of a longest facial path in \(G\). Jendroľ in 2018 proved that every simple \(3\)-connected plane graph

doi:10.7494/opmath.2020.40.4.475
fatcat:xhdhlewytbh6rg3slwfdu6wea4