On the maximum number of copies of H in graphs with given size and order
We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H) is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this pr...
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| Published in | Journal of graph theory Vol. 96; no. 1; pp. 34 - 43 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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| Abstract | We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H) is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this problem, when the host graph is bipartite. |
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| AbstractList | We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H) is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this problem, when the host graph is bipartite. Abstract We study the maximum number of copies of a graph in graphs with a given number of vertices and edges. We show that for any fixed graph is asymptotically realized by the quasi‐clique provided that the edge density is sufficiently large. We also investigate a variant of this problem, when the host graph is bipartite. |
| Author | Nagy, Dániel T. Vizer, Máté Patkós, Balázs Gerbner, Dániel |
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| Cites_doi | 10.1007/BF02772673 10.1016/j.jctb.2019.01.001 10.1007/BF02761855 10.1145/3188745.3188778 10.1016/S0012-365X(02)00878-6 10.1017/S0963548316000389 10.1016/0012-365X(86)90214-1 10.1007/BF01902206 10.1016/j.jctb.2016.03.004 10.1016/0012-365X(92)90323-8 10.1007/s10955-017-1804-0 |
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| References | 2018; 55.2 2019; 82 1986; 62 2017; 26 1986; 53 1978; 32 1992; 103 2017; 168.2 2019; 137 1981; 38 2018 2016; 121 2001; 38 1992; 27 2003; 265 e_1_2_5_15_1 e_1_2_5_14_1 e_1_2_5_9_1 e_1_2_5_16_1 e_1_2_5_8_1 e_1_2_5_11_1 Füredi Z. (e_1_2_5_10_1) 1992; 27 e_1_2_5_6_1 e_1_2_5_5_1 e_1_2_5_12_1 e_1_2_5_4_1 e_1_2_5_3_1 e_1_2_5_2_1 Gerbner D. (e_1_2_5_13_1) 2019; 82 Bollobás B. (e_1_2_5_7_1) 2001; 38 Reiher C. (e_1_2_5_17_1) 2018; 55 |
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| Snippet | We study the maximum number ex(n,e,H) of copies of a graph H in graphs with a given number of vertices and edges. We show that for any fixed graph H,ex(n,e,H)... Abstract We study the maximum number of copies of a graph in graphs with a given number of vertices and edges. We show that for any fixed graph is... |
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| SubjectTerms | Apexes bipartite graph extremal graph theory Graph theory Graphs number of subgraphs quasi‐clique |
| Title | On the maximum number of copies of H in graphs with given size and order |
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