Iren Darijani

activity

20142022

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4 papers · 1 filter

math.CO2022

Block colourings of star systems

Robert F. Bailey, Iren Darijani

An $e$ -star system of order $n$ is a decomposition of the complete graph $K_{n}$ into copies of the complete bipartite graph $K_{1, e}$ (or $e$ -star). Such systems are known to exist…

math.CO2022

Colourings of path systems

Iren Darijani, David A. Pike

A $P_{m}$ path in a graph is a path on $m$ vertices. A $P_{m}$ system of order $n > 1$ is a partition of the edges of the complete graph $K_{n}$ into $P_{m}$ paths. A $P_{m}$ system is said to…

math.CO2022

Arc-disjoint hamiltonian paths in Cartesian products of directed cycles

Iren Darijani, Babak Miraftab, Dave Witte Morris

We show that if $C_{1}$ and $C_{2}$ are directed cycles (of length at least two), then the Cartesian product $C_{1} □ C_{2}$ has two arc-disjoint hamiltonian paths. (This answers a ques…

math.CO2019

Colourings of star systems

Iren Darijani, David Pike

An $e$ -star is a complete bipartite graph $K_{1, e}$ . An $e$ -star system of order $n > 1$ , $S_{e} (n)$ , is a partition of the edges of the complete graph $K_{n}$ into $e$ -stars. An $e$ -sta…