Steiner Triple Systems with High Chromatic Index
نویسندگان
چکیده
منابع مشابه
5-Chromatic Steiner Triple Systems
We show that, up to an automorphism, there is a unique independent set in PG(5,2) that meet every hyperplane in 4 points or more. Using this result, we show that PG(5,2) is a 5-chromatic STS. Moreover, we construct a 5-chromatic STS(v) for every admissible v ≥ 127.
متن کاملComputing the Chromatic Index of Steiner Triple Systems
A Steiner triple system of order v, denoted STS (v), is a pair (V, B); V is a u-set of elements and B is a collection of 3-subsets of V called blocks. Each unordered pair of elements is contained in precisely one block. There is a substantial body of research on STS, partially because of their wide applicability in the design of experiments, and in the theory of error-correcting codes. In the d...
متن کاملCirculants and the Chromatic Index of Steiner Triple Systems
We complete the determination of the chromatic number of 6valent circulants of the form C(n; a, b, a+b) and show how this can be applied to improving the upper bound on the chromatic index of cyclic Steiner triple systems.
متن کاملThe triangle chromatic index of Steiner triple systems
In a Steiner triple system of order v, STS(v), a set of three lines intersecting pairwise in three distinct points is called a triangle. A set of lines containing no triangle is called triangle-free. The minimum number of triangle-free sets required to partition the lines of a Steiner triple system S, is called the triangle chromatic index of S. We prove that for all admissible v, there exists ...
متن کاملOn 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...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2017
ISSN: 0895-4801,1095-7146
DOI: 10.1137/17m1114338