Charles A. Cusack

Pebbling Algorithms in Diameter Two Graphs

Consider a connected graph and a configuration of pebbles on its vertices. A pebbling step consists of removing two pebbles from a vertex and placing one on an adjacent vertex. A configuration is called solvable if it is possible to place a pebble on any given vertex through a sequence of pebbling steps. A smallest number

Partial Steiner triple systems with equal-sized holes

t

The Complexity of Pebbling in Diameter Two Graphs

such that any configuration with

The Complexity Of Pebbling Reachability And Solvability In Planar And Outerplanar Graphs

t

Wildfire Wally: a volunteer computing game

pebbles is solvable is called the pebbling number of the graph. In this paper, we consider algorithms determining the solvability of a pebbling configuration on graphs of diameter two. We prove that if

Semiregular Large Sets

k

Doppelgangers and Lemke graphs

is the vertex connectivity of a diameter two graph

Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5

G

Group factorizations in cryptography

, then a configuration is solvable if there are at least

Ray tracing as an object-oriented example for CS 1

c(k)=min{k+4,3k-1}