This quote from the paper I'm currently reading:
by θ-subgraph we mean a subgraph homeomorphic to $K_{\{3,2\}}$
I'm familiar with $\theta_{i,j}$ denoting either a subgraph consisting of $i$ paths through at least $j$ edges with the same pair of endpoints; or the similar notion but with an additional requirement for the paths to be internally disjoint (usually explicitly stated.)
Thus, I have two questions:
- Where does the $\theta$ notation come from?
And,
- What does $K_{\{3,2\}}$ mean in the context of the quote?
It's possible that I'm missing something very obvious here; if that's the case, I'm sorry for the silly question.
The graph $K_{\{3,2\}}$ can be drawn to look like the Greek letter theta.
I presume that $K_{\{m,n\}}$ denotes the complete bipartite graph with $m$ vertices on one side and $n$ vertices on the other.