Cycles in k-traceable oriented graphs
Copyright policy )Cycles in k-traceable oriented graphs
A digraph of order at least \(k\) is said to be \(k\)-traceable if each of its sub-digraphs of order \(k\) is traceable. The paper presents some results pertaining to various cycle properties of strong \(k\)-traceable oriented graphs and investigates the extent to which pancyclicity is retained by strong \(k\)-traceable oriented graphs. In addition, it establishes an upper bound on the order of \(k\)-traceable oriented graphs having a strong component with girth greater than 3. It is also shown that the Path Partition Conjecture holds for 1-deficient oriented graphs having a strong component with girth at least 6.
- University of South Africa South Africa
- Converse College United States
- University of Winnipeg Canada
- University of Winnipeg Canada
oriented graph, Directed graphs (digraphs), tournaments, tournament, pancyclic digraph, \(k\)-traceable, k-traceable, path partition conjecture, Traceability Conjecture, Oriented graph, Tournament, Pancyclic digraph, Path Partition Conjecture, Paths and cycles, traceability conjecture
oriented graph, Directed graphs (digraphs), tournaments, tournament, pancyclic digraph, \(k\)-traceable, k-traceable, path partition conjecture, Traceability Conjecture, Oriented graph, Tournament, Pancyclic digraph, Path Partition Conjecture, Paths and cycles, traceability conjecture
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