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Graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects.

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3-colourability of Eulerian maximal planar graph

The key here is to note that the planar graph considered is maximal. Every vertex in this graph is adjacent to a triangle since every face of the graph is a triangle. Thus this is possible to extend t …
Xin Yuan Li's user avatar
4 votes
1 answer
153 views

Neighborly properties in a bipartite graph

Input: Let $G$ be a connected, bipartite graph with parts $A$ and $B$, each of size $n$. For a set of vertices $S$, let $N(S)$ be its set of neighbors. Question: Decide whether there exists a subset $ …
Xin Yuan Li's user avatar