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Results tagged with graph-theory
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user 27829
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.
3
votes
Accepted
chromatic number of a simple graph whose length of the longest odd cycle is 2k+1
Yes. If a graph $G$ is bipartite, by definition its chromatic number $\chi(G)$ is less than or equal to $2$. If $G$ contains an odd cycle, then $\chi(G) \leq l+1$, where $l$ is the length of a longest …
- 3,692
7
votes
Accepted
On the maximum number of $t$-subset of $\{1,\ldots, n\}$ having pairwise singleton or empty ...
Lucia's answer given in the linked question from the comment gives an upper bound (i.e., no pair should appear twice as a subset of $A_i$). But of course, the real question starts from here:
When can …
- 3,692