William Duckworth

On the approximability of the maximum induced matching problem

Abstract In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio d −1 for MIM in d -regular graphs, for each d ⩾3. We also prove that MIM is APX-complete in d -regular graphs, for each d ⩾3.

Minimum independent dominating sets of random cubic graphs

We present a heuristic for finding a small independent dominating set D of cubic graphs. We analyze the performance of this heuristic, which is a random greedy algorithm, on random cubic graphs using differential equations, and obtain an upper bound on the expected size of D. A corresponding lower bound is derived by means of a direct expectation argument. We prove that D asymptotically almost surely satisfies 0.2641n ≤ |D| ≤ 0.27942n.

On the Independent Domination Number of Random Regular Graphs

A dominating set

Connected domination of regular graphs

\cal D

Randomized greedy algorithms for finding small k-dominating sets of regular graphs

of a graph

Packing Edges in Random Regular Graphs

G

Large 2-Independent Sets of Regular Graphs

is a subset of

Small Edge Dominating Sets of Regular Graphs

V(G)

Small k-Dominating Sets of Regular Graphs

such that, for every vertex

On the Connected Domination Number of Random Regular Graphs

v\in V(G)