scholarly journals Towards Gallai's path decomposition conjecture

2020 ◽  
Author(s):  
Fábio Botler ◽  
Maycon Sambinelli
Keyword(s):  
Path Decomposition

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.

Structural path decomposition analysis of resource utilization in China, 1997–2017

2021 ◽  
Vol 322 ◽  
pp. 129006
Author(s):  
Junhua Zhang ◽  
Heming Wang ◽  
Lin Ma ◽  
Jian Wang ◽  
Jiashi Wang ◽  
...  
Keyword(s):  
Resource Utilization ◽  
Decomposition Analysis ◽  
Path Decomposition ◽  
Structural Path

Fluctuation identities for random walk by path decomposition at the maximum

1980 ◽  
Vol 12 (02) ◽  
pp. 291-293 ◽  
Author(s):  
Priscilla Greenwood ◽  
Jim Pitman
Keyword(s):  
Random Walk ◽  
Path Decomposition

scholarly journals A Path Decomposition for Markov Processes

1978 ◽  
Vol 6 (2) ◽  
pp. 345-348 ◽  
Author(s):  
P. W. Millar
Keyword(s):  
Markov Processes ◽  
Path Decomposition
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