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Results tagged with co.combinatorics
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user 160959
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
5
votes
1
answer
92
views
Is there any relationships between path cover number and chromatic number?
Let G be a finite simple graph. Consider the independent number $\alpha$, the chromatic number $\chi$ and the path cover number (also called the path partition number) $\rho$.
Then we have $\alpha\chi …
- 622
3
votes
1
answer
179
views
Property of the spanning tree with minimal leaves
Let $G$ be a connected simple graph. For any spanning tree $T$ of $G$, let $l(T)$ be the number of leaves of the graph $T$. Consider $\ell=\min_Tl(T)$, can I find a spanning tree $T$ with $l(T)=\ell$, …
- 622
2
votes
1
answer
363
views
Best known upper bound for the Ramsey function $R(k,x)$
The Ramsey function $R(k,x)$ is defined as the minimal integer $n$ such that any graph on $n$ vertices contains either a clique of size $k$ or an independent set of size $x$. Miklós Ajtai, János Koml …
- 622