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On the Simultaneous EdgeColoring Conjecture
, 2000
"... At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2simultaneous edgecoloring and conjectured that every bipartite graphic sequence, with all degrees at least 2, has a 2simultaneous edgecolorable realization. In fact, this conjecture is a reformulation o ..."
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Cited by 4 (1 self)
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At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2simultaneous edgecoloring and conjectured that every bipartite graphic sequence, with all degrees at least 2, has a 2simultaneous edgecolorable realization. In fact, this conjecture is a reformulation
THREE EDGECOLORING CONJECTURES
"... The focus of this article is on three of the author’s open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold. ..."
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The focus of this article is on three of the author’s open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.
On the EdgeColoring of Split Graphs
, 1996
"... We consider the following question: can split graphs with odd maximum degree be edgecoloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case the grap ..."
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We consider the following question: can split graphs with odd maximum degree be edgecoloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case
Edgecolorings
"... and circular flow numbers on regular graphs Eckhard Steffen∗ The paper characterizes (2t + 1)regular graphs with circular flow number 2 + 22t−1. For t = 1 this is Tutte’s characterization of cubic graphs with flow number 4. The class of cubic graphs is the only class of odd regular graphs where a f ..."
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flow number separates the class 1 graphs from the class 2 graphs. We finally state some conjectures and relate them to existing flowconjectures. 1
Rainbow edgecoloring and rainbow domination
, 2012
"... Let G be an edgecolored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edgechromatic number of G, written ˆχ ′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is ttolerant if it contains no monochroma ..."
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Let G be an edgecolored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edgechromatic number of G, written ˆχ ′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is ttolerant if it contains
Homomorphisms of 2edgecolored graphs
, 2009
"... In this paper, we study homomorphisms of 2edgecolored graphs, that is graphs with edges colored with two colors. We consider various graph classes (outerplanar graphs, partial 2trees, partial 3trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a ..."
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In this paper, we study homomorphisms of 2edgecolored graphs, that is graphs with edges colored with two colors. We consider various graph classes (outerplanar graphs, partial 2trees, partial 3trees, planar graphs) and the problem is to find, for each class, the smallest number of vertices of a
Optimal strong parity edgecoloring of complete graphs
"... A parity walk in an edgecoloring of a graph is a walk along which each color is used an even number of times. Let p(G) be the least number of colors in an edgecoloring of G having no parity path (a parity edgecoloring). Let �p(G) be the least number of colors in an edgecoloring of G having no op ..."
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no open parity walk (a strong parity edgecoloring). Always �p(G) ≥ p(G) ≥ χ ′ (G). We prove that �p(Kn) = 2 ⌈lg n ⌉ − 1 for all n. The optimal strong parity edgecoloring of Kn is unique when n is a power of 2, and the optimal colorings are completely described for all n.
Results 1  10
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377,281