PC-Trees and Planar Graphs
PC-Trees and Planar Graphs
PC-Trees and Planar Graphs
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28<br />
Some coloring theorems of Kneser hypergraphs<br />
AUTHOR: Peng-An Chen 陳鵬安<br />
Department of Mathematics, National Taitung University, Taitung, Taiwan<br />
pengan@nttu.edu.tw<br />
ABSTRACT<br />
In 2004, Matouˇsek provided a fascinating combinatorial proof of the Kneser conjecture.<br />
Ziegler (2002) extended the scope of Matouˇsek’s approach, by establishing a combinatorial<br />
proof of the hypergraph coloring theorem of Dol’nikov (1981). He also provided a<br />
combinatorial proof of Schrijver’s theorem (1978). In this paper, we prove some coloring<br />
theorems of Kneser hypergraphs via the Octahedral Tucker’s lemma <strong>and</strong> the Octahedral<br />
Fan’s lemma.<br />
KEYWORDS: Kneser hypergraphs, Dol’nikov theorem, Octahedral Tucker’s lemma,<br />
Octahedral Fan’s lemma
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