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Minimum degree conditions for large subgraphs

Allen, Peter, Böttcher, Julia, Hladký, Jan and Cooley, Oliver (2009) Minimum degree conditions for large subgraphs. Electronic Notes in Discrete Mathematics, 34. pp. 75-79. ISSN 1571-0653

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Identification Number: 10.1016/j.endm.2009.07.013


Much of extremal graph theory has concentrated either on finding very small subgraphs of a large graph (such as Turán's theorem [Turán, P., On an extremal problem in graph theory (in Hungarian), Matematiko Fizicki Lapok 48 (1941), 436–452]) or on finding spanning subgraphs (such as Dirac's theorem [Dirac, G.A., Some theorems on abstract graphs, Proc. London Math. Soc. s3-2 (1952), 69–81] or more recently work of Komlós, Sárközy and Szemerédi [Komlós, J., G. N. Sárközy and E. Szemerédi, On the square of a Hamiltonian cycle in dense graphs, Random Struct. Algorithms 9 (1996), 193-211; Komlós, J., G. N. Sárközy and E. Szemerédi, Proof of the Seymour Conjecture for large graphs, Ann. Comb. 2 (1998), 43–60] towards a proof of the Pósa-Seymour conjecture). Only a few results give conditions to obtain some intermediate-sized subgraph. We contend that this neglect is unjustified. To support our contention we focus on the illustrative case of minimum degree conditions which guarantee squared-cycles of various lengths, but also offer results, conjectures and comments on other powers of paths and cycles, generalisations thereof, and hypergraph variants.

Item Type: Article
Official URL:
Additional Information: © 2009 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 May 2012 14:49
Last Modified: 20 Jul 2021 02:05

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