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Even Cycles in Graphs with Many Odd Cycles

✍ Scribed by Ralph J. Faudree; Evelyne Flandrin; Michael S. Jacobson; Jenő Lehel; Richard H. Schelp

Publisher
Springer Japan
Year
2000
Tongue
English
Weight
133 KB
Volume
16
Category
Article
ISSN
0911-0119

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📜 SIMILAR VOLUMES

Even cycles in graphs
Even cycles in graphs
✍ Joseph G. Conlon 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 888 KB

## Abstract Let __G__ be a 3‐connected simple graph of minimum degree 4 on at least six vertices. The author proves the existence of an even cycle __C__ in __G__ such that __G‐V__(__C__) is connected and __G‐E__(__C__) is 2‐connected. The result is related to previous results of Jackson, and Thomas

A note on odd/even cycles
A note on odd/even cycles
✍ Anna Lubiw 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 397 KB
Short odd cycles in 4-chromatic graphs
Short odd cycles in 4-chromatic graphs
✍ Nilli, A. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 163 KB 👁 3 views

It is shown that any 4-chromatic graph on n vertices contains an odd cycle of length smaller than √ 8n.

Small odd cycles in 4-chromatic graphs
Small odd cycles in 4-chromatic graphs
✍ Tao Jiang 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 50 KB

## Abstract It is shown that every 4‐chromatic graph on __n__ vertices contains an odd cycle of length less than $2\sqrt {n}\,+3$. This improves the previous bound given by Nilli [J Graph Theory 3 (1999), 145–147]. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 115–117, 2001