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 …

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.

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 coordinates.

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 …

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 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, …

Dec 5, 2020 · Edge coloring of a bipartite graph with a maximum degree of D requires only D colors As graphs are my Achilles' heel, I'm incapable to use the information contained in the above to prove …