Two Extremal Problems in Graph Theory
Keyword(s):
We consider the following two problems. (1) Let $t$ and $n$ be positive integers with $n\geq t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that contains neither $K_t$ nor $K_{t,t}$ as a subgraph. (2) Let $r$, $t$ and $n$ be positive integers with $n\geq rt$ and $t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that does not contain $r$ disjoint copies of $K_t$. Problem 1 for $n < 2t$ is solved by Turán's theorem and we solve it for $n=2t$. We also solve Problem 2 for $n=rt$.
Keyword(s):
2003 ◽
Vol 23
(3)
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pp. 225-234
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1983 ◽
Vol 34
(1)
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pp. 109-111
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1972 ◽
Vol 2
(2)
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pp. 183-186
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1999 ◽
Vol 75
(1)
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pp. 160-164
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1981 ◽
Vol 31
(1)
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pp. 111-114
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