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(2)
Complete Graph
Edge Coloring
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Interval edgecolorings of complete graphs and ndimensional cubes
Interval edgecolorings of complete graphs and ndimensional cubes,10.1016/j.disc.2010.02.001,Discrete Mathematics,Petros A. Petrosyan
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Interval edgecolorings of complete graphs and ndimensional cubes
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Citations: 2
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Petros A. Petrosyan
An edgecoloring of a graph G with colors 1,2,…,t is called an interval tcoloring if for each i∈{1,2,…,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this paper we show that if n=p2q, where p is odd, q is nonnegative, and 2n−1≤t≤4n−2−p−q, then the
complete graph
K2n has an interval tcoloring. We also prove that if n≤t≤n(n+1)2, then the ndimensional cube Qn has an interval tcoloring.
Journal:
Discrete Mathematics  DM
, vol. 310, no. 1011, pp. 15801587, 2010
DOI:
10.1016/j.disc.2010.02.001
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References
(14)
Investigation on Interval EdgeColorings of Graphs
(
Citations: 19
)
Armen S. Asratian
,
R. R. Kamalian
Journal:
Journal of Combinatorial Theory  JCT
, vol. 62, no. 1, pp. 3443, 1994
Proper pathfactors and interval edgecoloring of (3, 4)biregular bigraphs
(
Citations: 6
)
Armen S. Asratian
,
Carl Johan Casselgren
,
Jennifer Vandenbussche
,
Douglas B. West
Journal:
Journal of Graph Theory  JGT
, vol. 61, no. 2, pp. 8897, 2009
Lower bounds and a tabu search algorithm for the minimum deficiency problem
(
Citations: 4
)
Mathieu Bouchard
,
Alain Hertz
,
Guy Desaulniers
Journal:
Journal of Combinatorial Optimization  JCO
, vol. 17, no. 2, pp. 168191, 2009
The complexity of consecutive Dcoloring of bipartite graphs: 4 is easy, 5 is hard
(
Citations: 14
)
Krzysztof Giaro
Journal:
Ars Combinatoria  ARSCOM
, vol. 47, 1997
On the Deficiency of Bipartite Graphs
(
Citations: 10
)
Krzysztof Giaro
,
Marek Kubale
,
Michal Malafiejski
Journal:
Discrete Applied Mathematics  DAM
, vol. 94, no. 13, pp. 193203, 1999
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Citations
(2)
A note on upper bounds for the maximum span in interval edge colorings of graphs
Rafael R. Kamalian
,
Petros A. Petrosyan
Journal:
Computing Research Repository  CORR
, vol. abs/0911.5, 2009
Interval edge colorings of some products of graphs
Petros A. Petrosyan
Journal:
Computing Research Repository  CORR
, vol. abs/0911.4, 2009