The geometric simultaneous embedding problem asks whether two planar graphs on the same set of vertices in the plane can be drawn using straight lines, such that each graph is pla...
Sergio Cabello, Marc J. van Kreveld, Giuseppe Liot...
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
Abstract. Given a graph G and a nonnegative integer k, the NP-complete Induced Matching problem asks for an edge subset M such that M is a matching and no two edges of M are joined...
Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint sub...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...