Oct 13, 2015 · So I have the following graphs drawn. How can I tell whether they are bipartite? If it is bipartite, how to identify 2 disjoint non empty sets?

Apr 29, 2024 · How can we prove that a graph is bipartite if and only if all of its cycles have even order? Also, does this theorem have a common name? I found it in a maths Olympiad toolbox.

Oct 7, 2023 · 0 I am trying to intuitively understand why a bipartite graph in which every vertex has degree exactly $2$ is simply a cycle.

Jan 24, 2016 · Can someone explain to me with an example how to create the adjacency matrix of a bipartite graph? And why the diagonal elements of it are not zero? Thanks.

Jul 27, 2016 · Prove that all trees are bipartite [closed] Ask Question Asked 9 years, 7 months ago Modified 9 months ago

A regular bipartite graph has the same number of vertices in the two partions. So we need to add vertices also. I'm not sure that it is always possible to add edges to get a $\Delta$-regular bipartite …

Jul 26, 2011 · I am not sure how the definition of bipartite graph fits for these graphs. If they are bipartite where is the bipartition?

Aug 29, 2022 · Show that a $C_4$ -free bipartite graph between two vertex parts of sizes of $a$ and $b$ has at most $ab^ {1/2}+b$ edges. Let's introduce some basic notations: $\binom {X} {2}$ means …

Jul 24, 2024 · A bipartite graph has a unique bipartition (except for interchanging the two partite sets) if and only if it is connected. Let G be a bipartite graph. If u and v are vertices in distinct components, …

Jun 7, 2020 · Of course, the definition of "bipartite" is easily generalised to graphs that are not simple, and we might want to do this in some cases: for instance if we are studying graph colourability, we …