Talk:Biregular graph

Semi-regular

One has to be careful here. If semiregular means that the graph has two possible degree values, say x and y, then the notion bipartite semiregular is more general than biregular. Tomo (talk) 05:37, 9 December 2012 (UTC)

Agree. --MathsPoetry (talk) 19:29, 17 December 2012 (UTC)

Vertex count: wrong?

I might be stupid, but the vertex count property seems wrong to me. I end up with $x|U|=y|V|$ and not $y|U|=x|V|$.

The double counting proof is, according to me: the number of endpoints of edges in $U$ is $x|U|$, the number of endpoints of edges in $V$ is $y|V|$, and each edge contributes the same amount (one) to both numbers, hence $x|U|=y|V|$.

For example, on the complete bipartite graph $K_{3,2}$, $deg(U)=3$, $|U|=2$, $deg(V)=2$, $|V|=3$, and $3\times 2=2\times 3=6$.

What do I do wrong, or is the article wrong? --MathsPoetry (talk) 19:35, 17 December 2012 (UTC)

I think the article was wrong. I have changed it as you suggest. —David Eppstein (talk) 19:39, 17 December 2012 (UTC)

Thank you David. --MathsPoetry (talk) 19:40, 17 December 2012 (UTC)