A constrained path decomposition of cubic graphs and the path number of cacti

2013 ◽  
pp. 615-616
Author(s):  
Fábio Botler ◽  
Yoshiko Wakabayashi
Keyword(s):  
Cubic Graphs ◽  
Path Decomposition ◽  
Path Number

Path decompositions of digraphs

1974 ◽  
Vol 10 (3) ◽  
pp. 421-427 ◽  
Author(s):  
Brian R. Alspach ◽  
Norman J. Pullman
Keyword(s):  
Path Decomposition ◽  
The Family ◽  
Path Decompositions ◽  
Simple Paths ◽  
Equality Holding ◽  
Path Number

A path decomposition of a digraph G (having no loops or multiple arcs) is a family of simple paths such that every arc of G lies on precisely one of the paths of the family. The path number, pn(G) is the minimal number of paths necessary to form a path decomposition of G.We show that pn(G) ≥ max{0, od(v)-id(v)} the sum taken over all vertices v of G, with equality holding if G is acyclic. If G is a subgraph of a tournament on n vertices we show that pn(G) ≤ with equality holding if G is transitive.We conjecture that pn(G) ≤ for any digraph G on n vertices if n is sufficiently large, perhaps for all n ≥ 4.

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

scholarly journals Path number of bipartite digraphs

1980 ◽  
Vol 28 (2) ◽  
pp. 243-244 ◽  
Author(s):  
William G Frye ◽  
Renu Laskar
Keyword(s):  
Path Number
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