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Frontmatter
Edited by Allan Lo, University of Birmingham, Richard Mycroft, University of Birmingham, Guillem Perarnau, Universitat Politècnica de Catalunya, Barcelona, Andrew Treglown, University of Birmingham
Book:

Surveys in Combinatorics 2019

Published online:

17 June 2019

Print publication:

27 June 2019, pp i-iv
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Contents
Edited by Allan Lo, University of Birmingham, Richard Mycroft, University of Birmingham, Guillem Perarnau, Universitat Politècnica de Catalunya, Barcelona, Andrew Treglown, University of Birmingham
Book:

Surveys in Combinatorics 2019

Published online:

17 June 2019

Print publication:

27 June 2019, pp v-vi
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Preface
Edited by Allan Lo, University of Birmingham, Richard Mycroft, University of Birmingham, Guillem Perarnau, Universitat Politècnica de Catalunya, Barcelona, Andrew Treglown, University of Birmingham
Book:

Surveys in Combinatorics 2019

Published online:

17 June 2019

Print publication:

27 June 2019, pp vii-viii
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Edited by Allan Lo, Richard Mycroft, Guillem Perarnau, Andrew Treglown
Published online:

17 June 2019

Print publication:

27 June 2019
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This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, cryptography, matroids, incidence geometries and graph limits. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.

Triangle-Tilings in Graphs Without Large Independent Sets
Part of
- Extremal combinatorics
- Graph theory
JÓZSEF BALOGH, ANDREW McDOWELL, THEODORE MOLLA, RICHARD MYCROFT
Journal:

Combinatorics, Probability and Computing / Volume 27 / Issue 4 / July 2018

Published online by Cambridge University Press:

09 May 2018, pp. 449-474
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We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an n-vertex graph G with sublinear independence number. In this setting, we show that if δ(G) ≥ n/3 + o(n), then G has a triangle-tiling covering all but at most four vertices. Also, for every r ≥ 5, we asymptotically determine the minimum degree threshold for a perfect triangle-tiling under the additional assumptions that G is Kr-free and n is divisible by 3.

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