# Questions tagged [co.combinatorics]

Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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### A different version of list coloring

Consider a non-regular bipartite graph $G$ . We consider list edge coloring the edges of the graph by giving lists of cardinality $max(deg(v_i),deg(v_j))+2$ for each edge $e=v_iv_j$ where $deg(v_i)$ ...
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### Reference request - parallel rectangles discrepancy theory

I've been reading about discrepancy theory and trying to understand some of the open problems in the field. Wikipedia has a list of some of the open problems, but the descriptions are terrible. In ...
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### Subset of $[\omega]^\omega$ that can be “colored” with $3$, but not $2$ colors

Let $[\omega]^\omega$ denote the set of infinite subsets of $\omega$. Let $S\subseteq [\omega]^\omega$. We say that a map $c:\omega \to \{0,\ldots,n-1\}$ is a coloring for $S$ with $n$ colors if ...
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### Cardinals realizable by the chromatic number of a regular hypergraph

For any set $X$ and cardinal $\kappa$, we denote by $[X]^\kappa$ the collection of subsets of $X$ having cardinality $\kappa$. If $H=(V,E)$ is a hypergraph, and $\kappa$ is a cardinal, we say that a ...
### Total Coloring of a graph with $\Delta\ge\frac{n}{2}$
Consider an even vertex transitive graph $G$, which is not complete, with order $n$ and degree $k$ greater than or equal to half the order. By Hajnal-Szemeredi theorem, we could partition the ...