Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms.… Expand

If (G, Phi) is a 3-connected plane graph, then chi sub c p* ( G, Phi)+ 9 is the minimum number of colors in any cyclic coloration of (G), and if rho* is sufficiently large of sufficiently large or sufficiently small, then this bound on chiSub c can be improved somewhat.Expand

We introduce the concept of variable degeneracy of a graph extending that of k-degeneracy. This makes it possible to give a common generalization of the point partition numbers and the list chromatic… Expand

An extension of a conjecture of Hobbs, a new proof of Tutte's theorem on 3-connected graphs, and a result on the existence of a vertex joined by edges to three vertices of a cycle in a graph are obtained.Expand

This result verifies the first unsettled case m=6 of the (m,1)-Minor Conjecture which is a weaker form of Hadwiger’s Conjectures and a special case of a more general conjecture of Chartrand et al.Expand

Hadwiger's Conjecture seems difficult to attack, even in the very special case of graphs G of independence number α (G) = 2. We present some results in this special case.

Abstract A graph G is clique-critical if G and G−x have different clique-graphs for all vertices x of G. For any graph H, there is at most a finite number of different clique-critical graphs G such… Expand