TY - JOUR
T1 - The Turán number of sparse spanning graphs
AU - Alon, Noga
AU - Yuster, Raphael
N1 - Funding Information:
E-mail addresses: [email protected] (N. Alon), [email protected] (R. Yuster). 1 Research supported in part by an ERC advanced grant, by a USA–Israeli BSF grant, and by the Israeli I-Core program.
PY - 2013/5
Y1 - 2013/5
N2 - For a graph H, the extremal number ex(n, H) is the maximum number of edges in a graph of order n not containing a subgraph isomorphic to H. Let δ(H)>0 and δ(H) denote the minimum degree and maximum degree of H, respectively. We prove that for all n sufficiently large, if H is any graph of order n with δ(H)≤n/40, then ex(n,H)=(n-12)+δ(H)-1. The condition on the maximum degree is tight up to a constant factor. This generalizes a classical result of Ore for the case H=Cn, and resolves, in a strong form, a conjecture of Glebov, Person, and Weps for the case of graphs. A counter-example to their more general conjecture concerning the extremal number of bounded degree spanning hypergraphs is also given.
AB - For a graph H, the extremal number ex(n, H) is the maximum number of edges in a graph of order n not containing a subgraph isomorphic to H. Let δ(H)>0 and δ(H) denote the minimum degree and maximum degree of H, respectively. We prove that for all n sufficiently large, if H is any graph of order n with δ(H)≤n/40, then ex(n,H)=(n-12)+δ(H)-1. The condition on the maximum degree is tight up to a constant factor. This generalizes a classical result of Ore for the case H=Cn, and resolves, in a strong form, a conjecture of Glebov, Person, and Weps for the case of graphs. A counter-example to their more general conjecture concerning the extremal number of bounded degree spanning hypergraphs is also given.
KW - Packing
KW - Spanning subgraph
KW - Turan number
UR - http://www.scopus.com/inward/record.url?scp=84877138545&partnerID=8YFLogxK
U2 - 10.1016/j.jctb.2013.02.002
DO - 10.1016/j.jctb.2013.02.002
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AN - SCOPUS:84877138545
SN - 0095-8956
VL - 103
SP - 337
EP - 343
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
IS - 3
ER -