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Coloring random graphs online without creating monochromatic subgraphs

✍ Scribed by Torsten Mütze; Thomas Rast; Reto Spöhel

Book ID: 112187423
Publisher: John Wiley and Sons
Year: 2012
Tongue: English
Weight: 600 KB
Volume: 44
Category: Article
ISSN: 1042-9832
DOI: 10.1002/rsa.20445

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## 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