scholarly journals Path Decompositions of Tournaments

2021 ◽  
pp. 195-200
Author(s):  
António Girão ◽  
Bertille Granet ◽  
Daniela Kühn ◽  
Allan Lo ◽  
Deryk Osthus
Keyword(s):  
Path Decompositions

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 Path decompositions of digraphs and their applications to Weyl algebra

2015 ◽  
Vol 67 ◽  
pp. 36-54 ◽  
Author(s):  
Askar Dzhumadil'daev ◽  
Damir Yeliussizov
Keyword(s):  
Weyl Algebra ◽  
Path Decompositions

scholarly journals On path decompositions of 2 k -regular graphs

2015 ◽  
Vol 50 ◽  
pp. 163-168 ◽  
Author(s):  
Fábio Botler ◽  
Andrea Jiménez
Keyword(s):  
Regular Graphs ◽  
Path Decompositions

scholarly journals Path decompositions and Gallai's conjecture

2005 ◽  
Vol 93 (2) ◽  
pp. 117-125 ◽  
Author(s):  
Genghua Fan
Keyword(s):  
Path Decompositions

One-dimensional Brownian motion and the three-dimensional Bessel process

1975 ◽  
Vol 7 (03) ◽  
pp. 511-526 ◽  
Author(s):  
James W. Pitman
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Bessel Process ◽  
Simple Path ◽  
Radial Part ◽  
One Dimensional ◽  
Path Decompositions

A simple path transformation is described which connects one-dimensional Brownian motion with the radial part of three-dimensional Brownian motion. This provides simple proofs of various path decompositions for these processes described by David Williams.

scholarly journals On the chromatic index of path decompositions

2004 ◽  
Vol 284 (1-3) ◽  
pp. 107-121 ◽  
Author(s):  
Peter Danziger ◽  
Eric Mendelsohn ◽  
Gaetano Quattrocchi
Keyword(s):  
Chromatic Index ◽  
Path Decompositions

Mixing markovian laws; with an application to path decompositions†

Stochastics ◽  
1983 ◽  
Vol 9 (3) ◽  
pp. 223-231 ◽  
Author(s):  
P. Salminen
Keyword(s):  
Path Decompositions
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