Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is th...
We investigate a variant of on-line edge-coloring in which there is a fixed number of colors availableandtheaimistocolorasmanyedgesaspossible.Weproveupperandlowerboundsontheperform...
This paper introduces a new strategy for playing the marking game on graphs. Using this strategy, we prove that if G is a planar graph, then the game colouring number of G, and he...
In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assign...
Jean Cardinal, Vlady Ravelomanana, Mario Valencia-...