Counting paths in digraphs

Journal Article · Fri Jan 01 00:00:00 EST 2010 · European Journal of Combinatorics

OSTI ID:971587

Sullivan, Blair D ^[1]; Seymour, Dr. Paul Douglas ^[2]

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1. ORNL
2. Princeton University

Say a digraph is k-free if it has no directed cycles of length at most k, for k {element_of} Z{sup +}. Thomasse conjectured that the number of induced 3-vertex directed paths in a simple 2-free digraph on n vertices is at most (n-1)n(n+1)/15. We present an unpublished result of Bondy proving there are at most 2n{sup 3}/25 such paths, and prove that for the class of circular interval digraphs, an upper bound of n{sup 3}/16 holds. We also study the problem of bounding the number of (non-induced) 4-vertex paths in 3-free digraphs. We show an upper bound of 4n{sup 4}/75 using Bondy's result for Thomasse's conjecture.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: Work for Others (WFO)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 971587
• Journal Information: European Journal of Combinatorics, Vol. 31, Issue 3
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
DIAGRAMS
LIMITING VALUES
BOUNDARY CONDITIONS