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%I #9 Aug 15 2019 16:56:09
%S 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,
%T 392,159,4,1,4,26,375,2130,4895,3855,1060,1,4,37,1061,14039,68696,
%U 113774,64669,12378,9,1,5,58,3331,103927,1140623,3953535,4607132
%N Triangle read by rows: T(n,k) = number of graphs on n node with edge chromatic number k (n >= 1, k >= 1).
%D Gupta, R. P. "The Chromatic Index and the Degree of a Graph." Notices Amer. Math. Soc. 13, 719, 1966.
%D Holyer, I. "The NP-Completeness of Edge Colorings." SIAM J. Comput. 10, 718-720, 1981.
%D 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.
%H Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeChromaticNumber.html">Edge Chromatic Number</a>
%e Triangle (transposed) begins:
%e k..|.n=..1..2..3..4...5...6....7.....8.......9.......10
%e --------------------------------------------------------
%e 1..|.....1..1..1..1...1...1....1.....1.......1........1
%e 2..|.....0..1..1..2...2...3....3.....4.......4........5
%e 3..|.....0..0..1..3...5..10...15....26......37.......58
%e 4..|.....0..0..1..5..14..46..123...375....1061.....3331
%e 5..|.....0..0..0..0..10..58..347..2130...14039...103927
%e 6..|.....0..0..0..0...2..38..392..4895...68696..1140623
%e 7..|.....0..0..0..0...0...0..159..3855..113774..3953535
%e 8..|.....0..0..0..0...0...0....4..1060...64669..4607132
%e 9..|.....0..0..0..0...0...0....0.....0...12378..1921822
%e 10.|.....0..0..0..0...0...0....0.....0.......9...274734
%Y Diagonals give A126728-A126731.
%K nonn,tabf
%O 1,9
%A _Keith Briggs_, Nov 22 2006
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