5 citations · 8 across the 27 of their papers we have counts for
30 papers
Vertex-transitive closures of graphs
Martin Bachratý, Grahame Erskine, Štefánia Glevitzká +2
A vertex-transitive closure of is a vertex-transitive supergraph of on the same vertex set. The vertex-transitive number of a graph , denoted by , is the smal…
The general position number of digraphs
Ullas Chandran S. V., Gabriele Di Stefano, Grahame Erskine +3
The general position number for graphs ask for largest vertex subsets such that no three vertices are contained on a common shortest path. We examine this problem in the settin…
Hat guessing with proper colorings
Sam Adriaensen, Peter Bentley, Anurag Bishnoi +6
We initiate the study of the hat guessing number of a graph where the adversary is only allowed to provide a proper coloring of the graph. This is the largest number for which…
There are no excess one digraphs
Slobodan Filipovski, Arnau Messegué, Josep M. Miret +1
A digraph is \emph{-geodetic} if for any pair there is at most one -walk of length not exceeding . The order of a -geodetic digraph with minimum ou…
Solution to some conjectures on mobile position problems
Ethan Shallcross, James Tuite, Aoise Evans +2
The general position problem for graphs asks for the largest number of vertices in a subset of a graph such that for any and any shortest -p…
Moving through Cartesian products, coronas and joins in general position
Sandi Klavžar, Aditi Krishnakumar, Dorota Kuziak +3
The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was de…
The General Position Problem: A Survey
Ullas Chandran S. V., Sandi Klavžar, James Tuite
Inspired by a chessboard puzzle of Dudeney, the general position problem in graph theory asks for a largest set of vertices in a graph such that no three elements of lie on…
Monophonic position sets of Cartesian and lexicographic products of graphs
Ullas Chandran S. V., Sandi Klavžar, Neethu P. K. +1
The general position problem in graph theory asks for the number of vertices in a largest set of vertices of a graph such that no shortest path of contains more than tw…
Colouring a graph with position sets
Ullas Chandran S. V., Gabriele Di Stefano, Haritha S. +2
In this paper we consider a colouring version of the general position problem. The \emph{$\gp $-chromatic number} is the smallest number of colours needed to colour the vertices of…
Lower General Position in Cartesian Products
Eartha Kruft Welton, Sharif Khudairi, James Tuite
A subset of vertices of a graph is in \emph{general position} if no shortest path in contains three vertices of . The \emph{general position problem} consists of fin…
On bipartite -mixed graphs
C. Dalfó, G. Erskine, G. Exoo +2
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which t…
General position polynomials
Vesna Iršič, Sandi Klavžar, Gregor Rus +1
A subset of vertices of a graph is a general position set if no triple of vertices from the set lie on a common shortest path in . In this paper we introduce the general pos…
Builder-Blocker General Position Games
Sandi Klavžar, Jing Tian, James Tuite
This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker,…
On large regular (1,1,k)-mixed graphs
C. Dalfó, G. Erskine, G. Exoo +4
An -mixed graph has every vertex with undirected degree , directed in- and out-degree , and diameter . In this paper, we study the case , proposing som…
Lower General Position Sets in Graphs
Gabriele Di Stefano, Sandi Klavžar, Aditi Krishnakumar +2
A subset of vertices of a graph is a \emph{general position set} if no shortest path in contains three or more vertices of . In this paper, we generalise a problem o…
Mutually avoiding Eulerian circuits
Grahame Erskine, Terry Griggs, Robert Lewis +1
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…
The maximum Wiener index of a uniform hypergraph
Stijn Cambie, Ervin Győri, Nika Salia +2
The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected -vertex…
On the Vertex Position Number of Graphs
Maya Thankachy, Elias John Thomas, Ullas Chandran +3
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 of a connected graph , we say that a set…
Traversing a graph in general position
Sandi Klavžar, Aditi Krishnakumar, James Tuite +1
Let be a graph. Assume that to each vertex of a set of vertices a robot is assigned. At each stage one robot can move to a neighbouring vertex. Then is a…
On the General Position Number of Mycielskian Graphs
Elias John Thomas, Ullas Chandran, James Tuite +1
The general position problem for graphs was inspired by the no-three-in-line problem from discrete geometry. A set of vertices of a graph is a \emph{general position set} i…
Small graphs and hypergraphs of given degree and girth
Grahame Erskine, James Tuite
The search for the smallest possible -regular graph of girth has a long history, and is usually known as the cage problem. This problem has a natural extension to hypergraph…
The structure of digraphs with excess one
James Tuite
A digraph is \emph{-geodetic} if for any (not necessarily distinct) vertices there is at most one directed walk from to with length not exceeding . The orde…
On networks with order close to the Moore bound
James Tuite, Grahame Erskine
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} p…
On some extremal position problems for graphs
James Tuite, Elias John Thomas, Ullas Chandran S. V.
The general position number of a graph is the size of the largest set of vertices such that no geodesic of contains more than two elements of . The monophonic positi…