scholarly journals Scaffold for the polyhedral embedding of cubic graphs

2020 ◽  
Author(s):  
Flor Aguilar ◽  
Gabriela Araujo-Pardo ◽  
Natalia García-Colín
Keyword(s):  
Cubic Graphs ◽  
Polyhedral Embedding

scholarly journals On the genera of polyhedral embeddings of cubic graph

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Author(s):  
Gunnar Brinkmann ◽  
Thomas Tucker ◽  
Nico Van Cleemput
Keyword(s):  
Efficient Algorithm ◽  
Computational Results ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
High Genus ◽  
Theoretical Maximum ◽  
Polyhedral Embedding

In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient algorithm to compute all polyhedral embeddings of a given cubic graph and constructions for cubic graphs with some special properties of their polyhedral embeddings. Some key results are that even cubic graphs with a polyhedral embedding on the torus can also have polyhedral embeddings in arbitrarily high genus, in fact in a genus {\em close} to the theoretical maximum for that number of vertices, and that there is no bound on the number of genera in which a cubic graph can have a polyhedral embedding. While these results suggest a large variety of polyhedral embeddings, computations for up to 28 vertices suggest that by far most of the cubic graphs do not have a polyhedral embedding in any genus and that the ratio of these graphs is increasing with the number of vertices.

scholarly journals Reflexive coloring complexes for 3-edge-colorings of cubic graphs

2021 ◽  
Vol 344 (4) ◽  
pp. 112309
Author(s):  
Fiachra Knox ◽  
Bojan Mohar ◽  
Nathan Singer
Keyword(s):  
Cubic Graphs ◽  
Edge Colorings

scholarly journals Cyclically five-connected cubic graphs

2017 ◽  
Vol 125 ◽  
pp. 132-167 ◽  
Author(s):  
Neil Robertson ◽  
P.D. Seymour ◽  
Robin Thomas
Keyword(s):  
Cubic Graphs

Cubic Graphs with Large Girth

1989 ◽  
Vol 555 (1 Combinatorial) ◽  
pp. 56-62 ◽  
Author(s):  
N. L. BIGGS
Keyword(s):  
Cubic Graphs ◽  
Large Girth

scholarly journals An upper bound on the domination number of n-vertex connected cubic graphs

2009 ◽  
Vol 309 (5) ◽  
pp. 1142-1162 ◽  
Author(s):  
A.V. Kostochka ◽  
B.Y. Stodolsky
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Cubic Graphs

Splitter Theorems for Cubic Graphs

2006 ◽  
Vol 15 (03) ◽  
pp. 355 ◽  
Author(s):  
GUOLI DING ◽  
JINKO KANNO
Keyword(s):  
Cubic Graphs

scholarly journals Even cycles with prescribed chords in planar cubic graphs

1983 ◽  
Vol 44 (3) ◽  
pp. 275-280 ◽  
Author(s):  
Herbert Fleischner
Keyword(s):  
Cubic Graphs
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