arXiv subjects

Rok Erman

Publications and source records attributed to Rok Erman.

2 recordsLinked to original sources

arXiv2013

Choosability of the square of a planar graph with maximum degree four

We study squares of planar graphs with the aim to determine their list chromatic number. We present new upper bounds for the square of a planar graph with maximum degree $Δ\leq 4$. In particular $G^2$ is 5-, 6-, 7-, 8-, 12-, 14-choosable if the girth of $G$ is at least 16, 11, 9, 7, 5, 3 respectively. In fact we prove more general results, in terms of maximum average degree, that imply the results above.

math.CO↗

arXiv2008

Cyclic colorings of plane graphs with independent faces

Let G be a plane graph with maximum face size D. If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with D+1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors.

math.CO↗