5 papers
A survey of repositories in graph theory
Srinibas Swain, C. Paul Bonnington, Graham Farr +1
Since the pioneering work of R. M. Foster in the 1930s, many graph repositories have been created to support research in graph theory. This survey reviews many of these graph repos…
Non-separating Planar Graphs
Hooman R. Dehkordi, Graham Farr
A graph is a non-separating planar graph if there is a drawing of on the plane such that (1) no two edges cross each other in and (2) for any cycle in , any…
Powerful sets: a generalisation of binary matroids
Graham E. Farr, Andrew Y. Z. Wang
A set of binary vectors, with positions indexed by , is said to be a \textit{powerful code} if, for all , the number of vectors in that a…
Topological containment of the 5-clique minus an edge in 4-connected graphs
Rebecca Robinson, Graham Farr
The topological containment problem is known to be polynomial-time solvable for any fixed pattern graph , but good characterisations have been found for only a handful of non-tr…
The Sprague-Grundy function for some nearly disjunctive sums of Nim and Silver Dollar games
Graham Farr, Nhan Bao Ho
We introduce and analyse an extension of the disjunctive sum operation on some classical impartial games. Whereas the disjunctive sum describes positions formed from independent su…