Path decompositions of digraphs
1974 ◽
Vol 10
(3)
◽
pp. 421-427
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Keyword(s):
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.
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2000 ◽
Vol 41
(1)
◽
pp. 133-136
1988 ◽
Vol 62
(03)
◽
pp. 419-423
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Keyword(s):
1971 ◽
Vol 29
◽
pp. 258-259
◽
Keyword(s):
1990 ◽
Vol 48
(3)
◽
pp. 600-601
Keyword(s):
Keyword(s):