论文信息 - On the 2-parallel chromatic index of Steiner triple systems

On the 2-parallel chromatic index of Steiner triple systems

The 2-parallel chromatic index X" (8) is the minimum number of colours required to colour the blocks of a Steiner triple system 8 so that any two parallel blocks receive different colours. The value of X" (v) = min {X" (8) : 8 is an 8TS(v)} is determined for all admissible v.-It is further shown how the 2-parallel chromatic index is related to the independence number and a complete analysis for all 8T8(v), v ~ 15 is given.

Mike J. Grannell | Terry S. Griggs | Alexander Rosa | Peter Danziger

[1] Charles J. Colbourn,et al. Hanani triple systems , 1993 .

[2] C. Colbourn,et al. The chromatic index of cyclic Steiner 2-designs , 1982 .

[3] A. Street,et al. Combinatorics: room squares, sum-free sets, Hadamard matrices , 1972 .

[4] Douglas R Stinson,et al. Contemporary design theory : a collection of surveys , 1992 .

[5] M. Grannell,et al. Derived Steiner Triple Systems of Order 15 , 1985 .

[6] D. K. Ray-Chaudhuri,et al. Solution of Kirkman''s schoolgirl problem , 1971 .

[7] Louise D. Cummings,et al. Complete classification of the triad systems on fifteen elements , 1919 .

[8] N. S. Barnett,et al. Private communication , 1969 .

[9] Douglas R. Stinson,et al. 2000000 Steiner triple systems of order 19 , 1985 .

[10] N. Sauer,et al. Maximal Subsets of a given Set having No Triple in Common with a Steiner Triple System on the set , 1969, Canadian Mathematical Bulletin.

[11] Charles J. Colbourn,et al. Anti-mitre steiner triple systems , 1994, Graphs Comb..