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...
Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n â...
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-...