Zobrazeno 1 - 10
of 65
pro vyhledávání: '"ERSKINE, GRAHAME"'
Autor:
Erskine, Grahame, Griggs, Terry S.
Cycle switching is a particular form of transformation applied to isomorphism classes of a Steiner triple system of a given order $v$ (an $STS(v)$), yielding another $STS(v)$. This relationship may be represented by an undirected graph. An $STS(v)$ a
Externí odkaz:
http://arxiv.org/abs/2405.07750
Autor:
Erskine, Grahame, Griggs, Terry S.
Properties of the 62,336,617 Steiner triple systems of order 21 with a non-trivial automorphism group are examined. In particular, there are 28 which have no parallel class, six that are 4-chromatic, five that are 3-balanced, 20 that avoid the mitre,
Externí odkaz:
http://arxiv.org/abs/2401.13356
Two Eulerian circuits, both starting and ending at the same vertex, are avoiding if at every other point of the circuits they are at least distance 2 apart. An Eulerian graph which admits two such avoiding circuits starting from any vertex is said to
Externí odkaz:
http://arxiv.org/abs/2304.11021
Autor:
Thankachy, Maya, Thomas, Elias John, Chandran, Ullas, Tuite, James, Di Stefano, Gabriele, Erskine, Grahame
In this paper we generalise the notion of visibility from a point in an integer lattice to the setting of graph theory. For a vertex $x$ of a connected graph $G$, we say that a set $S \subseteq V(G)$ is an \emph{$x$-position set} if for any $y \in S$
Externí odkaz:
http://arxiv.org/abs/2209.00359
Autor:
Erskine, Grahame, Griggs, Terry
An l-good sequencing of a Steiner triple system of order v, STS(v), is a permutation of the points of the system such that no l consecutive points in the permutation contains a block. It is known that every STS(v) with v > 3 has a 3-good sequencing.
Externí odkaz:
http://arxiv.org/abs/2204.02732
Autor:
Erskine, Grahame, Tuite, James
The search for the smallest possible $d$-regular graph of girth $g$ has a long history, and is usually known as the cage problem. This problem has a natural extension to hypergraphs, where we may ask for the smallest number of vertices in a $d$-regul
Externí odkaz:
http://arxiv.org/abs/2201.07117
We begin the study of collections of three blocks which can occur in a symmetric configuration with block size 3, $v_3$. Formulae are derived for the number of occurrences of these and it is shown that the triangle, i.e. abf, ace, bcd is a basis. It
Externí odkaz:
http://arxiv.org/abs/2108.06795
Autor:
Tuite, James, Erskine, Grahame
The degree/diameter problem for mixed graphs asks for the largest possible order of a mixed graph with given diameter and degree parameters. Similarly the \emph{degree/geodecity} problem concerns the smallest order of a $k$-geodetic mixed graph with
Externí odkaz:
http://arxiv.org/abs/2108.05820
A digraph $G$ is \emph{$k$-geodetic} if for any pair of (not necessarily distinct) vertices $u,v \in V(G)$ there is at most one walk of length $\leq k$ from $u$ to $v$ in $G$. In this paper we determine the largest possible size of a $k$-geodetic dig
Externí odkaz:
http://arxiv.org/abs/2102.04957
Publikováno v:
J. Combin. Des. (2021), 1--27
The study of symmetric configurations $v_3$ with block size 3 has a long and rich history. In this paper we consider two colouring problems which arise naturally in the study of these structures. The first of these is weak colouring, in which no bloc
Externí odkaz:
http://arxiv.org/abs/2004.04514