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Results tagged with graph-theory
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user 19729
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.
1
vote
Is the empty graph a tree?
Some comments above discuss the question from the point of view of homology. I'd like to expand on these.
You might consider a tree to be an abstract simplicial complex of dimension at most 1 that ha …
- 3,407
0
votes
When does a graph underlie the Hasse diagram of a poset?
This is not an answer, but some context.
A somewhat related notion is that of comparability graphs: these are the graphs for which there is a poset $P$ on the vertex set such that $\{x,y\}$ is an edge …
- 3,407
6
votes
Does the hypergraph of subgroups determine a group?
As @Keith Kearnes says, the negative answer ought to be somewhere in Roland Schmidt's book. Unless I'm mistaken, it suffices to find two non isomorphic groups with isomorphic coset lattices. Indeed, …
- 3,407
3
votes
Accepted
Proving that the complement of a bipartite graph has chromatic number equal to clique number
According to this Wikipedia entry
the statement that $\chi(\overline{G}) = \omega(\overline{G})$ for all bipartite $G$ is actually equivalent to König's Theorem.
- 3,407
5
votes
A flag complex is contractible iff the underlying graph is....?
A nice graph theory lemma for showing homotopy equivalence that builds on the "clique starring" already discussed is stated as Lemma 3.2 of Alexander Engström's paper arXiv:math/0508148. I'll rephras …
- 3,407