Given a graph G = (V, E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V × V ) \ E such that the graph...
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G. We show that there is a subdivision...
A homogeneous set is a non-trivial module of a graph, i.e. a nonempty, non-unitary, proper vertex subset such that all its elements present the same outer neighborhood. Given two ...
Claudson F. Bornstein, Celina M. Herrera de Figuei...
Given a class of graphs, G, a graph G is a probe graph of G if its vertices can be partitioned into two sets, P (the probes) and N (the nonprobes), where N is an independent set, s...
David B. Chandler, Maw-Shang Chang, Ton Kloks, Van...