Gallai's Conjecture For Graphs of Girth at Least Four
Article first published online: 6 MAR 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 3, pages 256–274, March 2014
How to Cite
Harding, P. and McGuinness, S. (2014), Gallai's Conjecture For Graphs of Girth at Least Four. J. Graph Theory, 75: 256–274. doi: 10.1002/jgt.21735
- Issue published online: 6 JAN 2014
- Article first published online: 6 MAR 2013
- Manuscript Revised: 17 JAN 2013
- Manuscript Received: 20 SEP 2011
In 1966, Gallai conjectured that for any simple, connected graph G having n vertices, there is a path-decomposition of G having at most paths. In this article, we show that for any simple graph G having girth , there is a path-decomposition of G having at most paths, where is the number of vertices of odd degree in G and is the number of nonisolated vertices of even degree in G.