Packing paths in a $(λ+μ)K_{v+u}-λK_v$
Year: 2015
Type: preprint
Abstract: Following standard terminology, $λK_v$ is a multigraph on $v$ vertices such that $λ$ edges join each pair of vertices. Let $(λ+μ)K_{v+u}-λK_v$ be the graph $(V\cup U,E)$ with $|V|=v$, $|U|=u$, and $(λ+μ)-λ=μ$ edges between the vertices $x$ and $y$ if $x$ and $y$ both lie in $V$ and $λ+μ$ edges between $x$ and $y$ otherwise. The main result of this paper establishes necessary and sufficient conditions for an $m$-path decomposition of $(λ+μ)K_{v+u}-λK_v$.
Source: arXiv (Cornell University)
Authors: Asplund, John, Chaffee, Joe, Hammer, James M.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394639245