Hajós' graph-coloring conjecture: Variations and counterexamples
✍ Scribed by Paul A Catlin
- Book ID
- 107884106
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 514 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract In his recent work Thomassen [J Combin Theory Ser B 93 (2005), 95–105] discussed various refinements of Hajós conjecture. Shortly after Mohar [Electr J Combin 12 (2005), N15] provided an answer to Thomassen's Conjecture 6.5, and proposed a possible extension. The aim of this article is
## Seyffarth, K., Hajos' conjecture and small cycle double covers of planar graphs, Discrete Mathematics 101 (1992) 291-306. We prove that every simple even planar graph on n vertices has a partition of its edge set into at most [(n -1)/2] cycles. A previous proof of this result was given by Tao,
## Abstract Faudree and Schelp conjectured that for any two vertices __x, y__ in a Hamiltonian‐connected graph __G__ and for any integer __k__, where __n__/2 ⩽ __k__ ⩽ __n__ − 1, __G__ has a path of length __k__ connecting __x__ and __y__. However, we show in this paper that there are infinitely ma