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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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### 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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### Graphs “weak” in context of cutting subgraphs

Lately I've been looking into graphs (simple, undirected, finite) that are in some way weak when it comes to connectivity, that is: Let $G$ be a graph of order $n$. We'll say that $G$ is $k$-weak if ...
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### Treewidth related properties of a bipartite graph with bounded local crossing number and diameter

If a bipartite degree at most $3$ graph on $O(n^2)$ vertices with diameter at most $O(\log n)$ has property that every edge intersects at most $O(\log n)$ edges on a planar drawing then does any of ...
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### Why do we assume that $\mathcal{A}$ is an algebra in this 2003 paper of Bobkov and Tetali?

In the following paper (extended version here), at the beginning of section 3, the authors give two axioms about $\mathcal{A}$. Axiom 1 is about $\mathcal{A}$ being an algebra. I do not see where this ...
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### Diameter of Cayley graphs of finite simple groups

Babai, Kantor and Lubotzky proved in 1989 the following theorem (Sciencedirect link to article). THEOREM 1.1. There is a constant $C$ such that every nonabelian finite simple group $G$ has a set $S$ ...
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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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### Dinitz Conjecture extension to rectangles

The Dinitz Conjecture, which was proved later in a more general form by Galvin, stated that given an $n\times n$ array, its elements could be filled exactly like a latin square, where the elements in ...
23 views

### cycle structure of bounded genus graphs

Given fixed genus $k$ is there some $q=f(k)$ for which there are $q$ sets of cycles $S_1, S_2,.., S_q$ each cycle of $S_i$ uses only verticies of $V_i \subset V$ each $G[V_i]$ is planar $S_i$ is a ...

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