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Relative length of longest paths and longest cycles in triangle-free graphs. \ud

By Daniel Paulusma and K. Yoshimoto


In this paper, we study triangle-free graphs. Let G=(V,E) be an arbitrary triangle-free graph with minimum degree at least two and σ4(G)|V(G)|+2. We first show that either for any path P in G there exists a cycle C such that |VPVC|1, or G is isomorphic to exactly one exception. Using this result, we show that for any set S of at most δ vertices in G there is a cycle C such that SVC.\ud \u

Topics: Triangle-free graph, Cycle, Ore-condition, Relative length.
Publisher: Elsevier
Year: 2008
DOI identifier: 10.1016/j.disc.2007.03.070
OAI identifier: oai:dro.dur.ac.uk.OAI2:7425

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  3. (1997). Cycles and paths in triangle-free graphs, The Mathematics of Paul Erd?s II,
  4. (1991). Cycles and paths trough specified vertices in k-connected graphs,
  5. (1995). Cycles through prescribed vertices with large degree sum,
  6. (1981). Cycles through specified vertices of a graph,
  7. (1993). Cycles through specified vertices,
  8. (1997). Cycles through subsets with large degree sums,
  9. Degree conditions and a dominating longest cycle,
  10. (1984). Dominating cycles in bipartite graphs, Progress in graph theory
  11. (2000). Graph Theory, Second edition, Graduate Texts in Mathematics 173,
  12. (2002). Hamilton cycles in 1-tough triangle-free graphs,
  13. (2004). Long cycles in triangle-free graphs with prescribed independence number and connectivity,
  14. (1989). Longest cycles in triangle-free graphs,
  15. (1980). Longest Paths and Cycles in
  16. (1960). Note on hamiltonian circuits,
  17. (2004). On paths and cycles through specified vertices,
  18. (1995). Relative length of long paths and cycles in graphs with large degree sums,
  19. (2001). Relative length of longest paths and cycles in 3-connected graphs,
  20. (1982). Relative lengths of paths and cycles in k-connected graphs,

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