The square G2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph ...
A k-rainbow path in a graph with colored edges is a path of length k where each edge has a different color. In this note, we settle the problem of obtaining a constructive k-colori...
Domingos Dellamonica Jr., Colton Magnant, Daniel M...
Abstract. We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new ...
Abstract. We explore the effects of using graph width metrics as restrictions on the input to online problems. It seems natural to suppose that, for graphs having some form of bou...
The problem of characterizing all the testable graph properties is considered by many to be the most important open problem in the area of property-testing. Our main result in thi...