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Results tagged with graph-theory
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user 485983
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
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Number of $5^{-}$-neighbors of high-degree vertices in maximal planar graphs
We call a vertex with a degree no more than $k$ a $k^{-}$-vertex and a $k^{+}$-vertex if it has a degree at least $k$. By the discharging method, the researchers in graph theory obtained a series of r …
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Clique number of $k$-critical graphs
A graph $G$ is called a ${\it{k}}$-${\it{critical}}$ graph if $\chi(G)=k$ and for any proper subgraph $H$ of $G$ we have $\chi(H)<k$， where $\chi(G)$ denotes the chromatic number of $G$. The structure …
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Perfect matching decomposition algorithm for bipartite regular graphs
It is a well-known result that a bipartite graph can be decomposed into edge-disjoint perfect matchings if and only if it is regular. Now here comes the question. Given a bipartite regular graph, is t …
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