# A Conjecture On Small Embeddings Of Partial Steiner Triple Systems

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### Workshop Cycles and Colourings 2007

The so-called Minimax Conjecture states that the representation number of a graph can be expressed by the clique covering numbers of the subgraphs, induced by the neighborhood sets of the vertices. We give partial results, in connection with this conjecture. Ramsey numbers for disjoint union of some graphs Halina Bielak

### Introduction - web.mat.bham.ac.uk

T. There are a large number of partial results on Conjecture 1.1, some focusing on special classes of trees and some on embedding a (small) proportion of the trees (see e.g. [4, 6, 15, 23, 25, 40, 44]). Possibly the most striking results towards Conjecture 1.1 have been obtained for the case of bounded degree trees.

### Partial Steiner triple system embeddings

Partial Steiner triple system embeddings Abstract Bryant, Gunasekara and Horsley have a reduction which we recap in this paper. 1. Introduction A partial Steiner triple system of order u, or PSTS(u), is a pair (U;A) where U is a set of uelements and Ais a set of

### arxiv-export-lb.library.cornell.edu

Ringel s tree packing conjecture in quasirandom graphs Peter Keevash Katherine Stadeny April 9, 2021 Abstract We prove that any quasirandom graph with nvertices and rnedges can

### P. J. Cameron: Publications

[12] Another characterisation of the small Janko group, J. Math. Soc. Japan 25 (1973), 591 595. [13] Characterisations of some Steiner systems, parallelisms and biplanes, Math. Z. 136 (1974), 31 39. [14] Locally symmetric designs, Geometriae Dedicata 3 (1974), 65 76.

### List of accepted abstracts

Javad Nikmehr. On the Coloring of Steiner Triple Systems Saieed Akbari, Maryam Ghanbari, Raoofeh Manaviyat and Sanaz Zare Firoozabadi. On the lucky labeling of Graphs Saieed Akbari. On the List Version of Generalized 1-2-3 Conjecture Fusun Akman and Papa Sissokho. The lattice of nite vector space parti-tions Mehdi Alaeiyan and M. K. Hosseinipoor.

### oparu.uni-ulm.de

Overview The theme of decomposing mathematical objects appears in nearly every eld of math-ematics. Not surprisingly, it is also a vibrant research area in discrete mathematics an

### On determining when small embeddings of partial Steiner

a family of counterexamples to a conjecture concerning when small embeddings exist. 1 Introduction A partial Steiner triple system of order u, or PSTS(u), is a pair (U;A) where Uis a set of u

### web.mat.bham.ac.uk

A BLOW-UP LEMMA FOR APPROXIMATE DECOMPOSITIONS JAEHOON KIM, DANIELA KUHN, DERYK OSTHUS, AND MYKHAYLO TYOMKYN Abstract. We develop a new method for constructing approximate decomp

### Monday - LSU Math

48A-B Je Bonn, Ordering Steiner Triple Systems and the Codes of Their Points 50 David R. Berman, Sandra C. McLaurin, Douglas D. Smith*, Fair Team Tournaments 11:20{11:35 148 Jeannette Janssen, Partial List Colourings of Graphs with Bounded Degree E113 Sam Greenberg, Multiple Matchings

### arXiv

arXiv:1604.07282v1 [math.CO] 25 Apr 2016 A BLOW-UP LEMMA FOR APPROXIMATE DECOMPOSITIONS JAEHOON KIM, DANIELA KUHN, DERYK OSTHUS, AND MYKHAYLO TYOMKYN¨ Abstract. We develop a new

### Embeddings of partial Steiner triple systems: best-possible

Embeddings of partial Steiner triple systems (L K 2 was decomposed into triangles) The blind problem Problem For what values of v does every PSTS(u) have an embedding of

### www.researchgate.net

Finite Fields and Their Applications 33 (2015) 29 36 Contents lists available at ScienceDirect Finite Fields and Their Applications. www.elsevier.com/locate/ﬀa. A

### arXiv

arXiv:1604.07282v3 [math.CO] 27 Sep 2017 A BLOW-UP LEMMA FOR APPROXIMATE DECOMPOSITIONS JAEHOON KIM, DANIELA KUHN, DERYK OSTHUS, AND MYKHAYLO TYOMKYN¨ Abstract. We develop a new

### ee g a o e

3.25 3.45 T. S. Griggs Representing graphs in Steiner triple systems 4.20 4.40 N. Korpelainen Linear clique-width for subclasses of cographs, with connec-tions to permutations 4.45 5.05 E. Rivera-Campo A class of odd-graceful trees 4.45 5.05 S. M. Hegde A proof of harmonious tree conjecture WIN1-02 Time Speaker Title

### 36ACCMCCProgramme

14:00 Daniel Horsley Embeddings of partial Steiner triple systems: best-possible and better Small order spreads of W(5,q) The Merino-Welsh Conjecture for

### Open Research Online

orientable biembeddings of the 80 nonisomorphic Steiner triple systems of order 15. Inﬁnite classes of speciﬁc Steiner triple systems that are known to appear in biembeddings are somewhat rare. It is known that systems obtained from the Bose construction have self-embeddings in both orientable and nonorientable surfaces [10, 14].

### Finite Geometries Fifth Irsee Conference

Extension Sets, A ne Designs, and Hamada s Conjecture Dieter Jungnickel University of Augsburg (Joint work with Yue Zhou and Vladimir D. Tonchev) Hamada s conjecture states that the p-rank of any design with the parameters of a geometric design PG k(d;q) or AG k(d;q), where qis a power of a prime p, is greater than or equal to the p-rank of the

### Index to Volume 8 - COnnecting REpositories

RODL, V., Small spaces with large point character 55 RONAN, M. A., Embeddings and hyperplanes of discrete geometries 179 ROSENGREN, A. and LINDSTROM, B., A combinatorial series expansion for the Ising model 317 SHA WE-TAYLOR, J., Automorphism groups of primitive distance-bitransitive graphs are almost simple 187 SHRIKHANDE, S. S.,

### Doctoral Degrees Conferred 1995 1996

Steiner triple systems. Kirkpatrick, Kimberly, Small graph de-compositions. Pike, David A., Hamilton decompositions of graphs. Raines, Michael Edwin, Embedding partial extended triple systems and partial totally symmetric quasigroups. Rinker, Susan Serrano, Multi two-path designs. Wu, Yi-Hong, Discrete logarithm cryp-tosystems.

### arXiv:1805.06767v3 [math.LO] 5 Nov 2019

A Steiner triple system is a set Stogether with a collection B of subsets of Sof size 3 such that any two elements of Sbelong to exactly one element of B. It is well known that the class of ﬁnite Steiner triple systems has a Fra¨ıss´e limit M F. Here we show that the theory T∗ Sq of M F is the model completion of the theory of Steiner

### The embedding problem for partial Steiner triple systems

on embeddings of partial Steiner triple systems with many partial results on the conjecture being obtained. In 1980 Andersen et al [1] proved that Lindner s Conjecture holds for a large family of partial Steiner triple systems, and that it holds when v ≥ 4u+1. This lower bound was recently reduced to 3u − 2 in [2].

### European Journal of Combinatorics Index, Volume 23

European Journal of Combinatorics Index, Volume 23 AHLSWEDE, R., BEY, C., ENGEL, K. and KHACHATRIAN, L. H.,The t-intersection Problem in the Truncated Boolean Lattice

### P. J. Cameron: Publications

[12] Another characterisation of the small Janko group, J. Math. Soc. Japan 25 (1973), 591 595. [13] Characterisations of some Steiner systems, parallelisms and biplanes, Math. Z. 136 (1974), 31 39. [14] Locally symmetric designs, Geometriae Dedicata 3 (1974), 65 76.

### Daniel Horsley - Monash University

[24] D. Horsley, Embedding Partial Steiner Triple Systems with Few Triples, SIAM J. Discrete Math. 28 (2014), 1199{1213. [23] D. Horsley, Small Embeddings of Partial Steiner Triple Systems, J. Combin.

### Decomposabletwofoldtriplesystemswith non-Hamiltonian2

is bipartite exactly when the TTS is decomposable to two Steiner triple systems. Any connected bipartite 2-BIG with noHamilton cycle is a counter-example to a conjecture posedbyTuttein1971. Ourmainresultisthatthereexists anintegerN suchthatfor all v > N, if v ≡ 1 or 3(mod6) then there exists a TTS(v) whose 2-BIG is bipartite

### (Aula) - EUROCOMB 2019

10:30 10:55 Z. L. Nagy: Spreading linear triple systems and expander triple systems (Juraj Bosák Room) 10:55 11:20 C. Pelekis: A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems (JB Room) 11:20 11:45 T. Mészáros: Exploring projective norm graphs (Juraj Bosák Room)