Joe Chaffee

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math.CO2016

Decomposition of a complete bipartite multigraph into arbitrary cycle sizes

John Asplund, Joe Chaffee, James Hammer

In a graph $G$ , let $μ_{G} (x y)$ denote the number of edges between $x$ and $y$ in $G$ . Let $λ K_{v, u}$ be the graph $(V \cup U, E)$ with $∣ V ∣ = v$ , $∣ U ∣ = u$ , and \[ μ_G(xy)=\begin{cases} λ…

math.CO2015

Packing paths in a $(λ + μ) K_{v + u} - λ K_{v}$

John Asplund, Joe Chaffee, James M. Hammer

Following standard terminology, $λ K_{v}$ is a multigraph on $v$ vertices such that $λ$ edges join each pair of vertices. Let $(λ + μ) K_{v + u} - λ K_{v}$ be the graph $(V \cup U, E)$ with $|V|=…

Decomposition of a complete bipartite multigraph into arbitrary cycle sizes

Packing paths in a (λ+μ)Kv+u​−λKv​

Packing paths in a $(λ + μ) K_{v + u} - λ K_{v}$