Spanning paths and cycles in triangle-free graphs

  • P. Mafuta
  • J. Mushanyu
Keywords: leaf number, minimum degree, Hamiltonicity, traceability


Let G bea triangle-free graph of order n and minimum degree δ > n/3. We will determine all lengths of cycles occurring in G. In particular, the length of a longest cycle or path in G is exactly the value admitted by the independence number of G. This value can be computed in time O(n 2.5) using the matching algorithm of Micali and Vazirani. An easy consequence is the observation that triangle-free non-bipartite graphs with δ⩾38n are hamiltonian.

Mathematics Subject Classification (2010): 05C05, 05C38, 05C45.


Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606