An embedding of a 3-regular graph in a surface is called polyhedral if its dual is a simple
graph. An old graph-coloring conjecture is that every 3-regular graph with a polyhedral …

A Grünbaum coloring of a triangulation G is a map c: such that for each face f of G, the three
edges of the boundary walk of f are colored by three distinct colors. By Four Color Theorem …

r-Dynamic Coloring on Snark Families Page 1 Journal of Physics: Conference Series PAPER
• OPEN ACCESS r-Dynamic Coloring on Snark Families To cite this article: CS Gomathi et al …

Abstract Mohar and Vodopivec [Combinatorics, Probability and Computing (2006) 15, 877-
893] proved that for every integer $ k $($ k\geq 1$ and $ k\neq 2$), there exists a snark …

Abstract The Four Color Theorem is equivalent with its dual form stating that each 2-edge-
connected 3-regular planar graph is 3-edge-colorable. In 1968, Grünbaum conjectured that …

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons
satisfying that the total angles at vertices are at least 2 π. The combinatorial information of …

The Continuing Saga of Snarks Page 1 The Continuing Saga of Snarks sarah-marie belcastro
sarah-marie belcastro (smbelcas@toroidalsnark.net) is a free-range mathematician and …

In the paper, we prove that for every integer n≥ 1, there exists a Petersen power P n with
nonorientable genus and Euler genus precisely n, which improves the upper bound of …