In this note we prove that every 2-connected graph of order n with no repeated cycle lengths has at most n + 2(n -2) -1 edges and we show this result is best possible with the correct order of magnitude on √ n. The 2connected case is also used to give a quick proof of Lai's result on the general cas
Planar Graphs Without Cycles of Specific Lengths
✍ Scribed by G. Fijavž; M. Juvan; B. Mohar; R. Škrekovski
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 208 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
It is easy to see that planar graphs without 3-cycles are 3-degenerate. Recently, it was proved that planar graphs without 5-cycles are also 3-degenerate. In this paper it is shown, more surprisingly, that the same holds for planar graphs without 6-cycles.
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