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Results tagged with graph-colorings
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user 136218
Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.
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Graphs with $n$ vertices and $m$ edges and more probable property
Following to my previous question on the same topic, I would like to have some opinions whether the present refinement have some chances to work or is doomed to fail.
Given the positive integers $n$ a …
- 990
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answer
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Improving a lower bound for the minimum of the maximum frequency of an element in a family o...
[Originally posted at math.stackexchange without answer]
Consider a family $\mathcal{F}$ of $n=|\mathcal{F}|$ sets, $\emptyset \not\in \mathcal{F}$ and an universe $U(\mathcal{F})$ of $q=|U(\mathcal{F …
- 990
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Do all graphs with $n$ vertices and $m$ edges have a special property?
Given the positive integers $n$ and $m$, consider the set of graphs $\mathcal{G} = \{G=(V,E): |V|=n \land |E|=m\}$.
For which values of $n$ and $m$ does the following requirement hold:
$\forall G \in …
- 990
1
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0
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Lower bound for the minimum of the maximum frequency of an element - with restrictions
Consider a family $\mathcal{F}$ of non-empty sets, with
$n=|\mathcal{F}|$ sets, $q=\left|\cup\mathcal{F}\right|$ elements in the universe, and $q\le n/4$.
It is known that of the $\binom{n}{2}$ ways t …
- 990