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

28 May 2018 to 1 June 2018
Koper
UTC timezone

## Decomposing complete multigraphs into stars of varying sizes

Not scheduled
15m
UP FHS (Koper)

### UP FHS

#### Koper

Titov trg 5,Koper

### Speaker

Dr Daniel Horsley (Monash University)

### Description

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.

### Primary authors

Dr Daniel Horsley (Monash University) Dr Rosalind Cameron (Memorial University)

### Presentation Materials

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