match_odd_vertices finds the shortest paths between all pairs of odd-degree vertices. Uses itertools.combinations to generate pairs of odd-degree vertices, then calls dijkstra to compute the shortest ...

The two vertices at the end of an edge in a graph must be different colors, not that all of the vertices of the graph must be different colors.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

These types of graphs are called trees. Ringel’s question was about the relationship between complete graphs and trees. He said: First imagine a complete graph containing 2 n + 1 vertices (that is, an ...

If on the other hand there are no odd-degree vertices, the script continues with the original graph. The third module applies the Boyer–Myrvold algorithm 33 and generates a planar embedding of ...

Graph theory describes systems where we have some collection of objects, usually represented as points or "vertices," in which pairs of objects may or may not be connected to each other, with ...

An overfull graph is a graph whose number of its edges is greater than the product of its maximum degree and [n/2] , where n is the number of vertices. In this paper, some extremals of overfull graphs ...