Questions tagged [extremal-graph-theory]
Study of graphs satisfying a property that are maximal or minimal with respect to some parameter. A classic example is Turán's Theorem, which exactly characterizes the densest graphs on $n$ vertices without a $K_t$ subgraph.
253 questions
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Suppose the independent number of a graph is bounded. How small the clique number can be?
Suppose the independent number of a graph is bounded. How small the clique number can be? linear?
It seems to be a natural problem to ask. but I could not find any reference.
Thanks.
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Minimal Non-planar Extensions of a Graph
Given a planar graph $G=(V,E)$ with vertices $V$ and edges $E$, call $\bar G = (V,\bar E)$ a non-planar extension of $G$ if $\bar G$ is non-planar and $E \subset \bar E$.
I'm interested in minimal ...
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Erdős–Stone theorem type edge density estimates for bipartite graphs?
The Erdős–Stone theorem theory says that the densest graph not containing a graph H (which has chromatic number r) has number of edges equal to $(r-2)/(r-1) {n \choose 2}$ asymptotically.
However, ...
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