A123962 Triangle read by rows: T(n,k) = number of graphs on n node with edge chromatic number k (n >= 1, k >= 1).

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

Offset

1,9

References

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.

Links

Table of n, a(n) for n=1..57.

Keith M. Briggs, Combinatorial Graph Theory

Eric Weisstein's World of Mathematics, Edge Chromatic Number

Example

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

Crossrefs

Diagonals give A126728-A126731.

Sequence in context: A007880 A004573 A242730 * A256888 A010585 A295302

Adjacent sequences: A123959 A123960 A123961 * A123963 A123964 A123965

Keyword

nonn,tabf

Author

Keith Briggs, Nov 22 2006

Status

approved