David A. Pike

Decycling Cartesian Products of Two Cycles

The decycling number

A deterministic version of the game of zombies and survivors on graphs

\nabla(G)

Hamilton decompositions of some line graphs

of a graph

Brushing without capacity restrictions

G

Hamilton cycles in restricted block-intersection graphs

is the smallest number of vertices which can be removed from

Twofold triple systems without 2-intersecting Gray codes

G

Edge searching weighted graphs

so that the resultant graph contains no cycles. In this paper, we study the decycling number for the family of graphs consisting of the Cartesian product of two cycles. We completely solve the problem of determining the decycling number of

On balanced incomplete block designs with specified weak chromatic number

C_m \square C_n

On cycle systems with specified weak chromatic number

for all

Twofold triple systems with cyclic 2-intersecting Gray codes

m