# Graphs, groups, and more: celebrating Brian Alspach’s 80th and Dragan Marušič’s 65th birthdays

from 28 May 2018 to 1 June 2018
Koper
UTC timezone
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# Decomposing complete multigraphs into stars of varying sizes

## Speakers

• Dr. Daniel HORSLEY

## Content

In 1979 Tarsi showed that an edge decomposition of a complete multigraph into stars of size $k$ exists whenever the obvious necessary conditions hold. In 1996 Lin and Shyu gave necessary and sufficient conditions for the existence of an edge decomposition of a (simple) complete graph into stars of sizes $m_1,\ldots,m_t$.

I will discuss the common generalisation of these problems: when does a complete multigraph admit an edge decomposition into stars of sizes $m_1,\ldots,m_t$? This problem exhibits more complicated and interesting behaviour than either of its specialisations.