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The number of 2-edge-colored complete graphs with unique hamiltonian alternating cycle

✍ Scribed by A. Benkouar; Y. Manoussakis; R. Saad

Book ID
108315807
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
132 KB
Volume
263
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

Edge-colored complete graphs with altern
Edge-colored complete graphs with alternating cycles
✍ S.H. Whitesides πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 648 KB

We prove that if the edges of the complete graph on n ~4 vertices are colored so that no vertex is on more than A edges of the same color, 1 c A < n -2,, then the graph has cycles of all lengths 3 through n with no A consecutive edges the same color.

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Cubic graphs with three Hamiltonian cycles are not always uniquely edge colorable
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## Abstract The generalized Petersen graph __P__(6__k__ + 3, 2) has exactly 3 Hamiltonian cycles for __k__ β‰₯ 0, but for __k__ β‰₯ 2 is not uniquely edge colorable. This disproves a conjecture of Greenwell and Kronk [1].

An upper bound on the number of edges of
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In this paper, we prove that any edge-coloring critical graph G with maximum degree ¿ (11 + √ 49 -24 )=2, where 6 1, has the size at least 3(|V (G)| -) + 1 if 6 7 or if ¿ 8 and |V (G)| ¿ 2 --4 -( + 6)=( -6), where is the minimum degree of G. It generalizes a result of Sanders and Zhao.