Example for adjacency matrix of a bipartite graph 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 $n$-cube is bipartite - Mathematics Stack Exchange 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
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 bipartite graph, even if we have the same number of vertices See the figure below B and E both have degree two, but we cannot make them degree 3 Am I right ?
Proof of Kőnigs line coloring theorem ($\chi (G) = \Delta (G)$) 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 $\chi' (G) = \Delta (G)$ myself
How can a bipartite graph be Eulerian? - Mathematics Stack Exchange So by definition a bipartite graph has some edges that are not used (i e the edges between vertices of the same set) That would then mean that there are unused edges and so the graph cannot be Eulerian
Complement of a bipartite graph - Mathematics Stack Exchange 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 then connect each vertex from the L to the R horizontally, then if I do the complement, it definitely still seems like a bipartite graph ?
How to identify bipartite graph from Adjacency matrix? 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, the graph isn't bipartite — quit and return NOT BIPARTITE