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Results tagged with extremal-graph-theory
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user 171032
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.
4
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Sizes of triangle-free graphs with independence number $k$
A triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. The independence number $α = α(G)$ of a graph $G$ is the cardinality of a maximum in dependent set of …
- 1,851
4
votes
1
answer
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Is there any study on the bounds on the number of even cycles for planar bipartite graphs?
In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).
[1] …
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1
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The upper bound of edges of the generalized cactus graphs
For $k=2,3,4$, we solved this question. But for large $k$, we may need more deep tools.
More details can be seen in L.C.Zhang, Y.Q. Huang, On the sizes of generalized cactus graphs, Discrete Applied …
- 1,851
4
votes
1
answer
341
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The upper bound of edges of the generalized cactus graphs
In graph theory, a cactus is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently, it is a connected graph in which every edge belongs to at most one simple …
- 1,851