The forcing number of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matching of G. In this paper, we demon...
The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s0, t0), . . . , (sk, tk), whether there are k + 1 pairwise disjoint paths P0, . . . , Pk, such tha...
This work introduces new bounds on the clique number of graphs derived from a result due to S´os and Straus, which generalizes the Motzkin-Straus Theorem to a specific class of h...
This paper presents an O(n2 ) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex de...
We observe that a formula given by S. Negami [Trans. Amer. Math. Soc. 299 (1987), 601-622] for the Tutte polynomial of a k-sum of two graphs generalizes to a colored Tutte polynom...