Cycles and Paths in Triangle-Free Graphs

Stephan Brandt ()
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Stephan Brandt: Freie Universität Berlin, Fachbereich Mathematik

A chapter in The Mathematics of Paul Erdős II, 2013, pp 81-93 from Springer

Abstract: Summary Let G be a 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 $$\delta \geq \frac{3} {8}n$$ are hamiltonian.

Keywords: Bipartite Graph; Minimum Degree; Longe Path; Hamiltonian Path; Maximum Match (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-7254-4_7

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