Erdos, Rubin, and Taylor found a nice correspondence between the minimum order of a complete bipartite graph that is not r-choosable and the minimum number of edges in an r-unifor...
Bounds on the minimum degree and on the number of vertices attaining it have been much studied for finite edge-/vertex-minimally kconnected/k-edge-connected graphs. We give an ove...
A k-stack layout (respectively, k-queue layout) of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing (non-nested) edges wi...
A dynamic coloring of a graph is a proper coloring of its vertices such that every vertex of degree more than one has at least two neighbors with distinct colors. The least number...
An equivalence graph is a disjoint union of cliques, and the equivalence number eq(G) of a graph G is the minimum number of equivalence subgraphs needed to cover the edges of G. W...