On Uniquely 4-Colorable Planar Graphs
A k-chromatic graph G is called uniquely k-colorable if every k-coloring of the vertex set V of G induces the same partition of V into k color classes. There is an innnite class C of uniquely…
Uniquely Total Colorable Graphs
- MathematicsGraphs Comb.
It is proved that if a graph G ≠ K2 is uniquely total colorable, then χ″(G) = Δ + 1, which supports the following conjecture: empty graphs, paths, and cycles of order 3k, k a natural number, are the only uniquely totalcolorable graphs.
Constructions of Uniquely 3-Colorable Graphs
- Mathematics2016 IEEE First International Conference on Data Science in Cyberspace (DSC)
This paper gives a simple counterexample on 16 vertices to S J Xu's conjecture concerning uniquely 3-colorable graphs without triangles, and based on this graph they construct an infinite family of uniquely3- colorable, 4-regular and triangle-free graphs by their construction methods.
Triangles in uniquely 3-colorable graphs on surfaces
- MathematicsAustralas. J Comb.
The finiteness of uniquely 3-colorable graphs on surfaces with high girth and a sufficient condition for the uniquely 3colorability of graph on surfaces are reported.
Size of edge-critical uniquely 3-colorable planar graphs
- MathematicsDiscret. Math.
A note on uniquely 3-colourable planar graphs
- MathematicsInt. J. Comput. Math.
It is proved that if a uniquely 3-colourable planar graph G has at most 4 triangles then G has two adjacent triangles.
SHOWING 1-10 OF 11 REFERENCES
Non-Separable and Planar Graphs.
- MathematicsProceedings of the National Academy of Sciences of the United States of America
A dual of a graph is defined by combinatorial means, and the paper ends with the theorem that a necessary and sufficient condition that a graph be planar is that it have a dual.
A SEMINAR ON GRAPH THEORY
Abstract : The opening six chapters present a coherent body of graph theoretic concepts. The remaining eight chapters report lectures presented by various seminar participants. Topics presented…
Planar Permutation Graphs
© Gauthier-Villars, 1967, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section B » (http://www.elsevier.com/locate/anihpb) implique l’accord avec les conditions…
Map Color Theorems
- Quart. J. Math
READ, An Introduction to Chromatic Polynomials
- J. Combinatorial Theory
On Colorings of Signed Graphs
- Elem. Math
NEY, Non-separable and Planar Graphs
- Trans. Amer. Math. Soc