New proofs of Konig's bipartite graph characterization theorem

Salman Ghazal

Abstract


We introduce four new elementary short proofs of the famous K\"{o}nig's theorem which characterizes bipartite graphs by absence of odd cycles. Our proofs are more elementary than earlier proofs because they use neither distances nor walks nor spanning trees.

Keywords


bipartite graph; odd cycle; path

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References


D. Ko ̈nig, Theorie der endlichen und unenlichen Graphen, Akademische Verlagsgesellschaft (1936).

R.Diestel, GraphTheory, Graduate Texts in Mathematics (2005). Springer. ISBN 978-3-642- 14278-9




DOI: http://dx.doi.org/10.19184/ijc.2017.1.2.4

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ISSN: 2541-2205

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