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Threecolor Ramsey numbers for paths, Combinatorica 27
, 2007
"... In February 2007 Fabricio Benevides [1] reported an easily correctable error in the proof of our main result. We wrote ([2], p. 2, lines 18 − 22) that one type of extremal colorings comes form an equal part blow up of a faktorization of K4. In fact, this blow up must not be necessarily equal part. A ..."
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Cited by 9 (4 self)
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In February 2007 Fabricio Benevides [1] reported an easily correctable error in the proof of our main result. We wrote ([2], p. 2, lines 18 − 22) that one type of extremal colorings comes form an equal part blow up of a faktorization of K4. In fact, this blow up must not be necessarily equal part. A similar coloring with A, B, C  ≥ (1 − α1) V (G)
Chromatic Index Critical Graphs of Orders 11 and 12
, 1997
"... A chromaticindexcritical graph G on n vertices is nontrivial if it has at most \Deltab n 2 c edges. We prove that there is no chromaticindexcritical graph of order 12, and that there are precisely two nontrivial chromatic index critical graphs on 11 vertices. Together with known results thi ..."
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Cited by 3 (1 self)
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A chromaticindexcritical graph G on n vertices is nontrivial if it has at most \Deltab n 2 c edges. We prove that there is no chromaticindexcritical graph of order 12, and that there are precisely two nontrivial chromatic index critical graphs on 11 vertices. Together with known results this implies that there are precisely three nontrivial chromaticindex critical graphs of order 12. 1 Introduction A famous theorem of Vizing [20] states that the chromatic index Ø 0 (G) of a simple graph G is \Delta(G) or \Delta(G) + 1, where \Delta(G) denotes the maximum vertex degree in G. A graph G is class 1 if Ø 0 (G) = \Delta(G) and it is class 2 otherwise. A class 2 graph G is (chromatic index) critical if Ø 0 (G \Gamma e) ! Ø 0 (G) for each edge e of G. If we want to stress the maximum vertex degree of a critical graph G we say G is \Delta(G)critical. Critical graphs of odd order are easy to construct while not much is known about critical graphs of even order. One reas...