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# Questions tagged [graph-theory]

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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### A specific collection of subgraphs in $K_{70, 70}$

Does there exist a collection of subgraphs $\{\Gamma_i\}_{i = 1}^{24}$ of $K_{70, 70}$, that satisfy the following two properties: 1)$\Gamma_i \cong K_{i, i} \forall 1 \leq i \leq 24$; 2)Any ...
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### Definition of k-partite hypergraph

I would like to know the standard definition of k-partite hypergraph. There are two natural generalizations of k-partite graph to k-partite hypergraph: 1. For all edges e, any two vertices in e are ...
169 views

### History of the Vertex Disjoint Cycle Cover with Minimal Edgeweight Sum

Questions: who first posed the problem of determining a collection of (directed) cycles, whose edgeweight sum is minimal and, for which each vertex belongs to exactly one of the cycles? who came up ...
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### What's the best method for sorting many multiple-characteristic items into multiple-characteristic bins? [on hold]

? There are 100 items to be sorted into just over 100 bins, where no bin has more than one item and not every bin is necessarily filled, but every item must be placed. ? There are certain items that ...

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