An orthogonal coloring of a graph G is a pair {c1, c2} of proper colorings of G, having the property that if two vertices are colored with the same color in c1, then they must hav...
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time,...
Algorithms are given for computing the number of n-element diagonal sets and the number of n-element strongly diagonal sets of binary sequences of length at most 2n - 2. The first...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Given a simple graph G, a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number i...