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Search: id:A123962
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| A123962 |
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Triangle read by rows: T(n,k) = number of graphs on n node with edge chromatic number k (n >= 1, k >= 1). |
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+0
5
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 1, 2, 5, 14, 10, 2, 1, 3, 10, 46, 58, 38, 1, 3, 15, 123, 347, 392, 159, 4, 1, 4, 26, 375, 2130, 4895, 3855, 1060, 1, 4, 37, 1061, 14039, 68696, 113774, 64669, 12378, 9, 1, 5, 58, 3331, 103927, 1140623, 3953535, 4607132
(list; graph; listen)
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OFFSET
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1,9
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REFERENCES
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Gupta, R. P. "The Chromatic Index and the Degree of a Graph." Notices Amer. Math. Soc. 13, 719, 1966.
Holyer, I. "The NP-Completeness of Edge Colorings." SIAM J. Comput. 10, 718-720, 1981.
Skiena, S. "Edge Colorings." Section 5.5.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 216, 1990.
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LINKS
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Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, Edge Chromatic number Number. This MathWorld page gives further citations and Mathematica loading and function for computing.
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EXAMPLE
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Triangle (transposed) begins:
k..|.n=..1..2..3..4...5...6....7.....8.......9.......10
--------------------------------------------------------
1..|.....1..1..1..1...1...1....1.....1.......1........1
2..|.....0..1..1..2...2...3....3.....4.......4........5
3..|.....0..0..1..3...5..10...15....26......37.......58
4..|.....0..0..1..5..14..46..123...375....1061.....3331
5..|.....0..0..0..0..10..58..347..2130...14039...103927
6..|.....0..0..0..0...2..38..392..4895...68696..1140623
7..|.....0..0..0..0...0...0..159..3855..113774..3953535
8..|.....0..0..0..0...0...0....4..1060...64669..4607132
9..|.....0..0..0..0...0...0....0.....0...12378..1921822
10.|.....0..0..0..0...0...0....0.....0.......9...274734
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CROSSREFS
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Diagonals give A126728-A126731.
Sequence in context: A030604 A007880 A004573 this_sequence A010585 A110879 A016587
Adjacent sequences: A123959 A123960 A123961 this_sequence A123963 A123964 A123965
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KEYWORD
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nonn,tabf
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AUTHOR
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Keith M. Briggs, Nov 22 2006
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