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)