discrete mathematics - How to tell if a graph is bipartite ...
Oct 13, 2015 · Why is this a problem? 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 …
Edge-coloring of bipartite graphs - Mathematics Stack Exchange
A theorem of König says that Any bipartite graph G has an edge-coloring with Δ(G) (maximal degree) colors. This document proves it on page 4 by: Proving the theorem for regular bipartite …
prove $n$-cube is bipartite - Mathematics Stack Exchange
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 …
Newest 'bipartite-graphs' Questions - Mathematics Stack Exchange
Connected bipartite graph which is neither path or (even) cycle must have a vertex of degree greater than $2$ Adjacency Matrix of Connected Bipartite Graph graph-theory matrix …
The dimension of root polytopes for bipartite graphs $G \subseteq …
4 days ago · Today, while reading Postnikov's work$^\color {magenta} {\star}$, I came across a question — why does the root polytope of a bipartite graph lie in an $ (m+n−2)$-dimensional …
Intuitive reason behind the fact that the definition of bipartite …
Jun 7, 2020 · Of course, the definition of "bipartite" is easily generalised to graphs that are not simple, and we might want to do this in some cases: for instance if we are studying graph …
Example for adjacency matrix of a bipartite graph
Jan 24, 2016 · Can someone explain to me with an example how to create the adjacency matrix of a bipartite graph? And why the diagonal elements of it are not zero? Thanks.
How to identify bipartite graph from Adjacency matrix?
Dec 8, 2017 · If the matrix is now in the canonical form of a bipartite adjacency matrix (where the upper-left and lower-right blocks are all zero), the graph is bipartite; quit and return …
Proof a graph is bipartite if and only if it contains no odd cycles
Apr 29, 2024 · How can we prove that a graph is bipartite if and only if all of its cycles have even order? Also, does this theorem have a common name? I found it in a maths Olympiad toolbox.
Proof of Kőnig's line coloring theorem ($\chi' (G) = \Delta (G)$)
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 …