We study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected ...

The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

Graph crossing numbers quantify the minimum number of edge intersections in any planar drawing of a graph, an essential parameter in both theoretical and applied graph theory. The study of crossing ...