𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Colored graphs without colorful cycles

✍ Scribed by Richard N. Ball; Aleš Pultr; Petr Vojtěchovský


Book ID
106167654
Publisher
Springer-Verlag
Year
2007
Tongue
English
Weight
281 KB
Volume
27
Category
Article
ISSN
0209-9683

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


Planar graph colorings without short mon
✍ Tomáš Kaiser; Riste Škrekovski 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 126 KB 👁 1 views

## Abstract It is well known that every planar graph __G__ is 2‐colorable in such a way that no 3‐cycle of __G__ is monochromatic. In this paper, we prove that __G__ has a 2‐coloring such that no cycle of length 3 or 4 is monochromatic. The complete graph __K__~5~ does not admit such a coloring. On

Coloring Graphs without Short Non-boundi
✍ S. Fisk; B. Mohar 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 357 KB

It is shown that there is a constant \(c\) such that if \(G\) is a graph embedded in a surface of genus \(g\) (either orientable or non-orientable) and the length of a shortest non-bounding cycle of \(G\) is at least \(c \log (g+1)\), then \(G\) is six-colorable. A similar result holds for three- an

Vertex colorings of graphs without short
✍ Andrzej Dudek; Reshma Ramadurai 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 118 KB 👁 1 views

Motivated by the work of Nešetřil and R ödl on "Partitions of vertices" we are interested in obtaining some quantitative extensions of their result. In particular, given a natural number r and a graph G of order m with odd girth g, we show the existence of a graph H with odd girth at least g and ord