On the average degree of critical graphs with maximum degree six
β Scribed by Lianying Miao; Jibin Qu; Qingbo Sun
- Book ID
- 113567365
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 186 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract Improper choosability of planar graphs has been widely studied. In particular, Ε krekovski investigated the smallest integer __g__~k~ such that every planar graph of girth at least __g__~k~ is __k__βimproper 2βchoosable. He proved [9] that 6ββ€β__g__~1~ β€β9; 5ββ€β __g__~2~ββ€β7; 5ββ€β__g__~3
## Abstract In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117β134; Russian Math Surveys 23 (1968), 125β142] conjectured that for any edge chromatic critical graph ${{G}} = ({{V}}, {{E}})$ with maximum degree $\Delta$, $|{{E}}| \geq {{{1}}\over {{2}}}\{(\Delta {{- 1}})|{{V}}| + {{3}}\}$. This conject