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Caccetta-Häggkvist’s Conjecture discusses the relation between the girth g(D) of a digraph D and the minimum outdegree δ + (D) of D. The special case when g(D) = 3 has lately attracted wide attention. For an undirected graph G, the binding number $bind(G)\geq \frac 3 2$ is a sufficient condition for G to have a triangle (cycle with length 3). In this paper we generalize the concept...
Let G = (V, E) be an edge-colored graph. A matching of G is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is NP-complete. This means that to find both sufficient and necessary good conditions for the existence of perfect heterochromatic...
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