Abstract
Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.
| Original language | English |
|---|---|
| Pages (from-to) | 185-207 |
| Number of pages | 23 |
| Journal | Journal of Graph Theory |
| Volume | 29 |
| Issue number | 3 |
| Publication status | Published - Nov 1998 |
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Keywords
- Dirac's Theorem
- Extremal graphs
- Turán's Theorem
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Extremal Graphs with Bounded Densities of Small Subgraphs. / Griggs, Jerrold R.; Simonovits, M.; Thomas, George Rubin.
In: Journal of Graph Theory, Vol. 29, No. 3, 11.1998, p. 185-207.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Extremal Graphs with Bounded Densities of Small Subgraphs
AU - Griggs, Jerrold R.
AU - Simonovits, M.
AU - Thomas, George Rubin
PY - 1998/11
Y1 - 1998/11
N2 - Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.
AB - Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.
KW - Dirac's Theorem
KW - Extremal graphs
KW - Turán's Theorem
UR - http://www.scopus.com/inward/record.url?scp=0032346396&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032346396&partnerID=8YFLogxK
M3 - Article
VL - 29
SP - 185
EP - 207
JO - Journal of Graph Theory
JF - Journal of Graph Theory
SN - 0364-9024
IS - 3
ER -