Filters








248 Hits in 5.2 sec

An improved product construction for large sets of Kirkman triple systems

S. Zhang, L. Zhu
2003 Discrete Mathematics  
It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive  ...  Kirkman triple system of order v, and an LR(u) is a new kind of design introduced by Lei.  ...  An improved construction for LKTS We ÿrst recall the deÿnition of LR-design [7] . Let X be a set of size u.  ... 
doi:10.1016/s0012-365x(02)00766-5 fatcat:rlyplkabtjc2nmqj7zgyub3j7e

Large sets of Kirkman triple systems with orderqn+2

C. Wang, C. Shi
2017 Discrete Mathematics  
The existence of Large sets of Kirkman Triple Systems (LKTS) is an old problem in combinatorics.  ...  The only known recursive constructions are an tripling construction by Denniston MR535159and a product construction by Lei MR1931492, both constructs an LKTS(uv) on the basis of an LKTS(v).  ...  A large set of Kirkman triple systems of order v, denoted by LKTS(v), is an LSTS(v) where each STS(v) is resolvable.  ... 
doi:10.1016/j.disc.2016.11.008 fatcat:e2hqm7tarzg3pmhvdwrqwa2gcy

Page 8081 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
[Zhu, Lie'] (PRC-SOO; Suzhou) An improved product construction for large sets of Kirkman triple systems. (English summary) Discrete Math. 260 (2003), no. 1-3, 307-313.  ...  Lei [Discrete Math. 257 (2002), no. 1, 63-81; MR 2003h:05041] that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS  ... 

Further results on large sets of Kirkman triple systems

Lijun Ji, Jianguo Lei
2008 Discrete Mathematics  
An LR design is introduced by the second author in his recent paper and it plays a very important role in the construction of LKTS (a large set of disjoint Kirkman triple system).  ...  Some constructions for these two designs are also presented. With the relationship between them and LKTS, we obtain some new LKTSs.  ...  Zhu for helpful suggestions on this topic and the referees for many helpful comments.  ... 
doi:10.1016/j.disc.2007.08.081 fatcat:zgwj7imc35cdhayalildu727yy

On colorful edge triples in edge-colored complete graphs [article]

Gábor Simonyi
2018 arXiv   pre-print
For the first two meaningful cases, when F=K_1,3 and F=P_4 we determine for infinitely many n the minimum number of colors needed for an F-caring edge-coloring of K_n.  ...  An explicit family of 2_2 n 3-edge-colorings of K_n so that every quadruple of its vertices contains a totally multicolored P_4 in at least one of them is also presented.  ...  Resolvable Steiner triple systems are called Kirkman triple systems (KTS for short) referring to Kirkman's puzzle in the middle of the 19th century asking for the existence of such a system of triples  ... 
arXiv:1812.06706v1 fatcat:j7tdg3hmi5h6fg6rneznw6hxfy

On Colorful Edge Triples in Edge-Colored Complete Graphs

Gábor Simonyi
2020 Graphs and Combinatorics  
For the first two meaningful cases, when $$F=K_{1,3}$$ F = K 1 , 3 and $$F=P_4$$ F = P 4 we determine for infinitely many n the minimum number of colors needed for an F-caring edge-coloring of $$K_n$$  ...  An edge-coloring of the complete graph $$K_n$$ K n we call F-caring if it leaves no F-subgraph of $$K_n$$ K n monochromatic and at the same time every subset of |V(F)| vertices contains in it at least  ...  Resolvable Steiner triple systems are called Kirkman triple systems (KTS for short) referring to Kirkman's puzzle in the middle of the 19th century asking for the existence of such a system of triples  ... 
doi:10.1007/s00373-020-02214-4 fatcat:tifalwbz5beofblin5zakv54ba

Transitive resolvable idempotent quasigroups and large sets of resolvable Mendelsohn triple systems

Yanxun Chang
2009 Discrete Mathematics  
Then we use TRIQ to present a tripling construction for large sets of resolvable Mendelsohn triple systems LRMTS(v)s, which improves an earlier version of tripling construction by Kang.  ...  As an application we obtain an LRMTS(4 · 3 n ) for any integer n ≥ 1, which provides an infinite family of even orders.  ...  Zhu for his helpful discussions on this topic. Research supported in part by NSFC Grant 10771013 and 10831002.  ... 
doi:10.1016/j.disc.2009.04.012 fatcat:v4gak2dpobbunbxys66tbffioa

Efficient Two-Stage Group Testing Algorithms for Genetic Screening

Michael Huber
2013 Algorithmica  
The main focus is on novel combinatorial constructions in order to minimize the number of individual tests at the second stage of a two-stage disjunctive testing procedure.  ...  Efficient two-stage group testing algorithms that are particularly suited for rapid and less-expensive DNA library screening and other large scale biological group testing efforts are investigated in this  ...  Acknowledgments The author thanks the anonymous referees for their careful reading and suggestions that helped improving the presentation of the paper.  ... 
doi:10.1007/s00453-013-9791-2 fatcat:xgleqxnr7fgwhkshrwdvnnhl7y

Linear spaces with many small lines

C.A. Rodger
1994 Discrete Mathematics  
In this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings.  ...  Also, it is shown that any linear space of order c can be embedded in a linear space of order about 13v in which there are no lines of size 2.  ...  Acknowledgment The author would like to thank Kevin Phelps and Rolf Rees for their useful comments during the preparation of this survey.  ... 
doi:10.1016/0012-365x(92)00511-o fatcat:6rzza6mlfnhrto72aw2q2hyhz4

Steiner quadruple systems - a survey

Charles C. Lindner, Alexander Rosa
1978 Discrete Mathematics  
However, several partial answers were given only 3 years later in 1847 by Kirkman [28] who showed that a system S(2,3, v) i(i.e. an STS) exists if and only if v = 1 or 3 (mod 6) and constructed systems  ...  A Steiner system S( t, k, O) is a pair (S, B) where S is a u-set and B is a collection of k-subsets of S such that every t-subset of S is contained in exactly one member of B.  ...  Any collection of triple systems (S, Tkj, (~5, Tzj, . . . , (S, Tkj SUC~I that T1 U 'If2 U l l . U Tk = T(S) is called a large set of STS. !  ... 
doi:10.1016/0012-365x(78)90122-x fatcat:hdr3ujbwrjetnclzfgmifwxzmy

Resolvable 2-designs for regular low-density parity-check codes

S.J. Johnson, S.R. Weller
2003 IEEE Transactions on Communications  
The resulting codes are ¡ ¢ -regular or £ ¢ -regular for any value of and for a flexible choice of code lengths.  ...  This paper extends the class of low-density paritycheck (LDPC) codes that can be algebraically constructed.  ...  Neal for his online repository of LDPCrelated software.  ... 
doi:10.1109/tcomm.2003.816946 fatcat:kgwy4b3pxrdkvaa2zg6yq54obi

Steiner systems $S(2,4,v)$ - a survey

Colin Reid, Alex Rosa
2010 Electronic Journal of Combinatorics  
We survey the basic properties and results on Steiner systems $S(2, 4, v)$, as well as open problems.  ...  OGP007268 (AR). the electronic journal of combinatorics (2010), #DS18  ...  The difficulty of constructing large sets of S(2, 4, v)s is partly due to the fact that the number of systems in a large set LS(2, 4, v) is quadratic in v.  ... 
doi:10.37236/39 fatcat:pnaqutsoz5ebhoppf6cm35hnaq

R.A.Fisher, design theory, and the Indian connection [article]

A.R.P.Rau
2009 arXiv   pre-print
This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.  ...  Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R. A. Fisher and of Indian mathematical statisticians in the 1930s.  ...  Kirkman constructed the solution with b = 35, these being the number of rows of three, 5 for each of the 7 days.  ... 
arXiv:0910.4163v1 fatcat:n52w6keffvhfpp6aov7oltvw4u

The triangle chromatic index of Steiner triple systems

Mike J. Grannell, Terry S. Griggs, Ray Hill
2001 The Australasian Journal of Combinatorics  
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.  ...  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.  ...  Acknowledgement The authors thank Professor Alex Rosa of McMaster University for his helpful comments and advice concerning the preparation of this paper.  ... 
dblp:journals/ajc/GrannellGH01 fatcat:y6knmyk76nebjgkcywc5zhqclu

Almost resolvable decompositions of 2Kn into cycles of odd length

Katherine Heinrich, C.C Lindner, C.A Rodger
1988 Journal of combinatorial theory. Series A  
We prove that there exists an almost resolvable m-cycle decomposition of 2K" + 1 for all odd ma3 and all S> 1. SC  ...  That is, they constructed what they called an almost resolvable 2-fold triple system of order n for all n = 1 (mod 3).  ...  When m = 3 and n is even the solution of the Oberwolfach problem is equivalent to finding a nearly Kirkman triple system for all n = 0 (mod 6).  ... 
doi:10.1016/0097-3165(88)90053-2 fatcat:avscrzbknfcjppke5o7hfjf6y4
« Previous Showing results 1 — 15 out of 248 results