We investigate a variant of on-line edge-coloring in which there is a fixed number of colors availableandtheaimistocolorasmanyedgesaspossible.Weproveupperandlowerboundsontheperform...
Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum...
We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order n is 5 n-1 3 . A known construction shows this number is best possible when n 1 mod...
We consider the problem of assigning a numerical channel to each transmitter in a large regular array such that multiple levels of interference, which depend on the distance betwe...
Let G be a graph with n vertices and independence number . Hadwiger's conjecture implies that G contains a clique minor of order at least n/. In 1982, Duchet and Meyniel prov...