4 citations · 11 across the 6 of their papers we have counts for
7 papers
A note on Hadwiger's conjecture: Another proof that every 4-chromatic graph has a minor
Daniel Cooper McDonald
The first non-obvious case of Hadwiger's Conjecture states that every graph with chromatic number at least 4 has a minor. We give a new proof that derives the minor…
Optimally reconnecting graphs against an edge-destroying adversary
Daniel C. McDonald
We introduce a model involving two adversaries Buster and Fixer taking turns modifying a connected graph, where each round consists of Buster deleting a subset of edges and Fixer r…
Connectedness and Hamiltonicity of graphs on vertex colorings
Daniel C. McDonald
Given a graph , let be the graph whose vertices are the proper -colorings of , with edges joining two colorings if contains a connected subgraph on at most…
List rankings and on-line list rankings of graphs
Daniel C. McDonald
A -ranking of a graph is a labeling of its vertices from such that any nontrivial path whose endpoints have the same label contains a larger label. The leas…
On-line vertex ranking of trees
Daniel C. McDonald
A -ranking of a graph is a labeling of its vertices from such that any nontrivial path whose endpoints have the same label contains a larger label. The leas…
A combinatorial proof on partition function parity
Daniel C. McDonald
One of the most basic results concerning the number-theoretic properties of the partition function is that takes each value of parity infinitely often. This statement…