Following [1], we investigate the problem of covering a graph G with induced subgraphs G1, . . . , Gk of possibly smaller chromatic number, but such that for every vertex u of G, ...
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
: Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player ...
The total chromatic number zt(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same colo...
We show that computing the crossing number of a graph with a given rotation system is NP-complete. This result leads to a new and much simpler proof of Hlinˇen´y’s result, tha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...