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.

Oct 13, 2015 · Well, bipartite graphs are precisely the class of graphs that are 2-colorable. Recall a coloring is an assignment of colors to the vertices of the graph such that no two adjacent …

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.

Mar 27, 2013 · Hint: If a graph is bipartite, it means that you can color the vertices such that every black vertex is connected to a white vertex and vice versa. Hint: Consider parity of the sum of …

Jul 27, 2016 · Prove that all trees are bipartite [closed] Ask Question Asked 9 years, 3 months ago Modified 5 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 …

Jan 29, 2015 · I thought a constraint would be that the graphs cannot be complete, otherwise the complements would be disconnected. but, if I take a bipartite graph with 4 vertices on each …

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 …

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.

Mar 16, 2018 · So by definition a bipartite graph has some edges that are not used (i.e. the edges between vertices of the same set). That would then mean that there are unused edges and so …