discrete mathematics - How to tell if a graph is bipartite ...
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?
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.
Edge-coloring of bipartite graphs - Mathematics Stack Exchange
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 …
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.
Prove that all trees are bipartite - Mathematics Stack Exchange
Jul 27, 2016 · Prove that all trees are bipartite [closed] Ask Question Asked 9 years, 6 months ago Modified 8 months ago
Are the graphs with no vertex and 1 vertex bipartite?
Jul 26, 2011 · I am not sure how the definition of bipartite graph fits for these graphs. If they are bipartite where is the bipartition?
Why is a bipartite graph in which every vertex has degree exactly
Oct 7, 2023 · we have a bipartite graph where every vertex has degree d = 2. This means that the graph is just a cycle of even length, which is a case that we’ve already covered in the first part.
Check whether a given graph is bipartite except for one edge
Nov 29, 2020 · Any cycle has at most |V| | V | edges, and if G G is bipartite except for one edge then the additional edge is in all odd-length cycles. We therefore try to remove each edge of …
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 …
Proving that $ \\chi(G) = \\omega(G) $ if $ \\bar{G} $ is bipartite.
Nov 23, 2015 · Note that it need not be true that χ(¯ G) = 2: the chromatic number of a bipartite graph is 1 if the graph has no edges. In that case G is a complete graph, and the result is …