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Graph Coloring Problems
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
Edge-colored saturated graphs
The maximum and minimum number of edges in such graphs are determined and the unique extremal graphs are characterized. Expand
Cyclic coloration of 3-polytopes
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
Variable degeneracy: extensions of Brooks' and Gallai's theorems
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 chromaticExpand
Non-separating induced cycles in graphs
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
Double-Critical Graphs and Complete Minors
It is proved that any non-complete double-critical $k$-chromatic graph is $6$-connected and contains a complete $k-graph as a minor. Expand
Any 7-Chromatic Graphs Has K7 Or K4,4 As A Minor
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
On a special case of Hadwiger's conjecture
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.
On clique-critical graphs
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 suchExpand