Related papers: Simple signed Steiner triple systems

Given a graph $G$ with a terminal set $R \subseteq V(G)$, the Steiner tree problem (STREE) asks for a set $S\subseteq V(G) \setminus R$ such that the graph induced on $S\cup R$ is connected. A split graph is a graph which can be partitioned…

About 5-15% of stellar systems are at least triple. About 1% of systems with a primary of $\tgs 1 \Mscun$ are triple with a {\it longer} peri od that is less than 30y, and so may in principle be capable of Roche-lobe overflow in both the…

An $(n,r,s)$-system is an $r$-uniform hypergraph on $n$ vertices such that every pair of edges has an intersection of size less than $s$. Using probabilistic arguments, R\"{o}dl and \v{S}i\v{n}ajov\'{a} showed that for all fixed integers…

We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions.

Let $\Gamma$ be a $G$-symmetric graph with vertex set $V$. We suppose that $V$ admits a $G$-partition $\mathcal{B} = \{ B_0, ... , B_b \}$, with parts of size $v$, and that the quotient graph induced on $\mathcal B$ is a complete graph of…

Signed difference sets have interesting applications in communications and coding theory. A $(v,k,\lambda)$-difference set in a finite group $G$ of order $v$ is a subset $D$ of $G$ with $k$ distinct elements such that the expressions…

Block-transitive Steiner $t$-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory,…

Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.

In this paper new Steiner systems $S(2,6,121)$, $S(2,6,126)$, $S(2,7,169)$ are introduced. Also some non-existence results for line lengths $7..11$ are presented. There is no solid proof that presented algorithm is exhaustive or correct,…

In this paper we make a partial progress on the following conjecture: for every $\mu>0$ and large enough $n$, every Steiner triple system $S$ on at least $(1+\mu)n$ vertices contains every hypertree $T$ on $n$ vertices. We prove that the…

In this paper, we obtain new lower and upper bounds for the problem of bipartite biregular cages. Moreover, for girth $6$, we give the exact parameters of the $(m,n;6)$-bipartite biregular cages when $n\equiv -1$ $\pmod m$ using the…

For a family ${\mathcal F}$ of $r$-graphs, let $\mathrm{ex}(n,{\mathcal F})$ denote the maximum number of edges in an ${\mathcal F}$-free $r$-graph on $n$ vertices. Let ${\mathcal F}_r(v,e)$ denote the family of all $r$-graphs with $e$…

A subset $D$ of the vertex set $V$ of a graph $G$ is called an $[1,k]$-dominating set if every vertex from $V-D$ is adjacent to at least one vertex and at most $k$ vertices of $D$. A $[1,k]$-dominating set with the minimum number of…

In this article, we show the existence of large sets $\operatorname{LS}_2[3](2,k,v)$ for infinitely many values of $k$ and $v$. The exact condition is $v \geq 8$ and $0 \leq k \leq v$ such that for the remainders $\bar{v}$ and $\bar{k}$ of…

In [C. Ding, An infinite family of Steiner systems $S(2,4,2^m)$ from cyclic codes, {\em J. Combin. Des.} 26 (2018), no.3, 126--144], Ding constructed a family of Steiner systems $S(2,4,2^m)$ for all $m \equiv 2 \pmod{4}$ from a family of…

In this paper we prove that a set of points $B$ of PG(n,2) is a minimal blocking set if and only if $<B>=PG(d,2)$ with $d$ odd and $B$ is a set of $d+2$ points of $PG(d,2)$ no $d+1$ of them in the same hyperplane. As a corollary to the…

A graph is prime (with respect to the split decomposition) if its vertex set does not admit a partition (A,B) (called a split) with |A|, |B| >= 2 such that the set of edges joining A and B induces a complete bipartite graph. We prove that…

The pasch configuration and Steiner triple systems

We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, \cite{S-W}.…

In answering questions from arXiv:0901.2337v1 we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V \to k be the corresponding standard…