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 theorem of König says that Any bipartite graph G G has an edge-coloring with Δ(G) Δ (G) (maximal degree) colors. This document proves it on page 4 by: Proving the theorem for 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.

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, …

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.

prove n n -cube is a bipartite graph for all n ≥ 1 n ≥ 1 This is a problem in my textbook and I cannot figure it out at all and have a test on graph theory tomorrow any help would be appreciated since I …

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, …

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 …

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 …