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Optimal induced universal graphs for bounded-degree graphs
Published online by Cambridge University Press: 11 October 2017
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
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.
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