9 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…
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…
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…
The General Position Problem: A Survey
Ullas Chandran S. V., Sandi Klavžar, Sandi Klavžar +1
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…
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…
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…