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?

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 …

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 …

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.

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.

Dec 25, 2025 · Today, while reading Postnikov's work$^\color {magenta} {\star}$, I came across a question — why does the root polytope of a bipartite graph lie in an $ (m+n−2)$-dimensional affine …

Dec 8, 2017 · If the matrix is now in the canonical form of a bipartite adjacency matrix (where the upper-left and lower-right blocks are all zero), the graph is bipartite; quit and return BIPARTITE. Otherwise, …

Oct 26, 2012 · So, any cycle in the bipartite graph can have atmost 2m vertices (follows from: Any bipartite graph always has an even cycle only). Hamiltonian cycle must cover all the vertices, so the …

Dec 25, 2025 · For questions about graphs for which the set of vertices can be divided into two disjoint subsets such that no edge of the graph joins two vertices from same subset.

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 side, and …