Given a graph and a single watchman, the objective of the Watchmanâ€™s Walk Problem is to find a closed dominating walk of minimum length which the watchman can traverse to efficiently guard the graph.â€¦ (More)

AHackenbush Sprig is a Hackenbush string with the ground edge coloured green and the remaining edges either red or blue. We show that in canonical form a Sprig is a star-based number (the ordinal sumâ€¦ (More)

A proper colouring is referred to as a Grundy colouring, or first-fit colouring if every vertex has a neighbour from each of the colour classes lower than its own. The Grundy number of a graph is theâ€¦ (More)