On odd circuits in 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

✍ 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

Totally Odd-subdivisions in 4-chromatic

Totally Odd-subdivisions in 4-chromatic Graphs

✍ Carsten Thomassen 📂 Article 📅 2001 🏛 Springer-Verlag 🌐 English ⚖ 363 KB

Packing Odd Circuits in Eulerian Graphs

✍ James F. Geelen; Bertrand Guenin 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 179 KB

Let C be the clutter of odd circuits of a signed graph ðG; SÞ: For nonnegative integral edge-weights w; we are interested in the linear program minðw t x: xðCÞ51; for C 2 C; and x50Þ; which we denote by (P). The problem of solving the related integer program clearly contains the maximum cut problem,

4-chromatic graphs with large odd girth

✍ Nguyen Van Ngoc; Zsolt Tuza 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 251 KB

It is known that the Mycielski graph can be generalized to obtain an infinite family of 4-chromatic graphs with no short odd cycles. The first proof of this result, due to Stiebitz, applied the topological method of Lov~sz. The proof presented here is elementary combinatorial.

On chromatic-choosable graphs

✍ Kyoji Ohba 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 70 KB

## Abstract A graph is chromatic‐choosable if its choice number coincides with its chromatic number. It is shown in this article that, for any graph __G__, if we join a sufficiently large complete graph to __G__, then we obtain a chromatic‐choosable graph. As a consequence, if the chromatic number