✦ LIBER ✦

On list coloring Steiner triple systems

✍ Scribed by P. E. Haxell; M. Pei

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 105 KB
Volume: 17
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20215

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study the list chromatic number of Steiner triple systems. We show that for every integer s there exists n~0~=n~0~(s) such that every Steiner triple system on n points STS(n) with n≥n~0~ has list chromatic number greater than s. We also show that the list chromatic number of a STS(n) is always within a log n factor of its chromatic number. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 314–322, 2009

📜 SIMILAR VOLUMES

Balanced Steiner Triple Systems

✍ Charles Colbourn; Lucien Haddad; Václav Linek 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 302 KB

and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press ## 1. Introduction A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that eve

A Steiner triple system which colors all

A Steiner triple system which colors all cubic graphs

✍ Mike Grannell; Terry Griggs; Martin Knor; Martin Škoviera 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 93 KB

## Abstract We prove that there is a Steiner triple system 𝒯 such that every simple cubic graph can have its edges colored by points of 𝒯 in such a way that for each vertex the colors of the three incident edges form a triple in 𝒯. This result complements the result of Holroyd and Škoviera that eve

On sparse countably infinite Steiner tri

On sparse countably infinite Steiner triple systems

✍ K. M. Chicot; M. J. Grannell; T. S. Griggs; B. S. Webb 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 107 KB 👁 1 views

## Abstract We give a general construction for Steiner triple systems on a countably infinite point set and show that it yields 2 nonisomorphic systems all of which are uniform and __r__‐sparse for all finite __r__⩾4. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 115–122, 2010

Skew-orthogonal steiner triple systems

✍ P. Dukes; E. Mendelsohn 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 302 KB 👁 1 views

Two Steiner triple systems, S 1 VY B 1 and S 2 VY B 2 , are orthogonal (S 1 c S 2 ) if B 1 B 2 Y and if fuY vg T fxY yg, uvwY xyw P B 1 , uvsY xyt P B 2 then s T t. The solution to the existence problem for orthogonal Steiner triple systems, (OSTS) was a major accomplishment in design theory. Two or

On the chromatic numbers of Steiner trip

On the chromatic numbers of Steiner triple systems

✍ Lucien Haddad 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB 👁 2 views

Geometric properties are used to determine the chromatic number of AG(4, 3) and to derive some important facts on the chromatic number of PG(n, 2). It is also shown that a 4-chromatic STS(v) exists for every admissible order v ≥ 21.

Ubiquitous configurations in Steiner tri

Ubiquitous configurations in Steiner triple systems

✍ Eric Mendelsohn; Alexander Rosa 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 347 KB 👁 1 views

A Steiner triple system S is a C-ubiquitous (where C is a configuration) if every line of S is contained in a copy of C, and is n-ubiquitous if it is C-ubiquitous for every n-line configuration C. We determine the spectrum of 4-ubiquitous Steiner triple systems as well as the spectra of C-ubiquitous