We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph ...
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that -----(u)(v) is an arc in H whenever...
A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long 2-colored paths in properly colored graphs. A modified version of the conjecture is ...
Let G be a undirected connected graph. Given a set of g groups each being a subset of V (G), tree routing and coloring is to produce g trees in G and assign a color to each of them...