It is known that the Mycielski graph can be generalized to obtain an infinite family of 4-chromatic graphs with no short odd cycles.
In this paper we deal with 4-chromatic graphs without short odd cycles. The first construction of this kind was published by Gallai [2]; those graphs have odd ...
4-chromatic Graphs with Large Odd Girth · N. Ngoc, Z. Tuza · Published in Discrete Mathematics 6 March 1995 · Mathematics.
Suppose G is a series-parallel graph. We prove that if G has odd girth at least 6k - 1 then χc(G) ≤ 8k/(4k - 1); if G has odd girth at least 6k + 1 then ...
4-chromatic graphs with large odd girth · Contents. Discrete Mathematics. Volume 138, Issue 1-3 · PREVIOUS ARTICLE. Pancyclicity of Hamiltonian line graphs.
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Graphs with Uncountable Chromatic Number. In the last section we constructed graphs with a large oddgirth and with high, even infinitely high, chromatic number.
It is known that the Mycielski graph can be generalized to obtain an infinite family of 4-chromatic graphs with no short odd cycles.
Dec 19, 2014 · What is the smallest 4-chromatic graph of girth 5? 18 · Does there exist a graph with maximum degree 8, chromatic number 8, clique number 6? 3.
A natural way to weaken the girth-condition is to require the graphs to have high odd-girth (the odd-girth is the length of a shortest odd cycle). How- ever, ...
Oct 20, 2015 · It is well known that there exist graphs with large chromatic number and girth. More precisely, for any k and l, there exists a graph G such that χ(G)>k.
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