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Optimal induced universal graphs for bounded-degree graphs

Published online by Cambridge University Press:  11 October 2017

NOGA ALON  and
RAJKO NENADOV
NOGA ALON
Affiliation:
Sackler School of Mathematics and Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. e-mail: nogaa@tau.ac.il
RAJKO NENADOV
Affiliation:
School of Mathematical Sciences, Monash University, VIC 3800, Australia. e-mail: rajko.nenadov@monash.edu
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Abstract

We show that for any constant Δ ≥ 2, there exists a graph Γ with O(nΔ / 2) vertices which contains every n-vertex graph with maximum degree Δ as an induced subgraph. For odd Δ this significantly improves the best-known earlier bound and is optimal up to a constant factor, as it is known that any such graph must have at least Ω(nΔ/2) vertices.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 1 , January 2019 , pp. 61 - 74
Copyright
Copyright © Cambridge Philosophical Society 2017 

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Footnotes

†

Research supported in part by a USA-Israeli BSF grant 2012/107, by an ISF grant 620/13 and by the Israeli I-Core program.

References

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