Mark Walters Research Page

A list of Publications and Submitted Papers

Submitted Papers

• Constructible Graphs and Pursuit
  Submitted
  Joint with Imre Leader and Maria-Romina Ivan.
  arXiv


• Optimal Resistor Networks
  Submitted
  Joint with J. Robert Johnson.
  

Published

• Product-free sets in the free semigroup
  European Journal of Combinatorics 83 (2020) P103003
  Joint with Imre Leader, Shoham Letzter, Bhargav Narayanan.
  Journal and arXiv


• Random Geometric Graphs and Isometries of Normed Spaces
  Transactions of the American Mathematical Society 370 (2018) P7361--7389
  Joint with Paul Balister, Béla Bollobás, Karen Gunderson and Imre Leader.
  Journal arXiv


• Transitive Avoidance games
  Electronic Journal of Combinatorics 24 (2017) P1.61
  Joint with J. Robert Johnson and Imre Leader.
  Journal Version arXiv


• An n-in-a-row type game
  Electronic Journal of Combinatorics 23 (2016) P3.7
  Joint with Joshua Erde
  Journal Version arXiv


• Sentry Selection in Sensor Networks: Theory and Algorithms
  International Journal of Sensor Networks (to appear)
  Joint with Paul Balister, Béla Bollobás, Martin Haenggi and Amites Sarkar.
  DOI 10.1504/IJSNET.2015.10001255


• Subtended Angles
  Israel Journal of Mathematics 214 (2016) 995–1012
  Joint with Paul Balister, Béla Bollobás, Zoltán Füredi and Imre Leader.
  DOI 10.1007/s11856-016-1370-1 arXiv


• Probably Intersecting Families are Not Nested
  Combinatorics, Probability and Computing 22 (2013) 146–160
  Joint with Paul A. Russell
  DOI 10.1017/S0963548312000387 Journal Version arXiv


• Small components in k-nearest neighbour graphs
  Discrete Applied Mathematics 160 (2012) 2037-2047
  Journal Version (DOI 10.1016/j.dam.2012.03.033) arXiv Local PDF


• The Evolution of Gaian Preferential Attachment Graphs
  ACITA'12 (conference paper)
  Joint with Paul Stone, Patrick Dantressangle and Abbe Mowshowitz


• Sharpness in the k-nearest neighbours random geometric graph model
  Advances in Applied Probability 44 (2012) 617–634
  Joint with Victor Falgas-Ravry
  DOI 10.1239/aap/1346955257
  Journal Version. arXiv Local PDF


• Transitive Sets in Euclidean Ramsey Theory
  Journal of Combinatorial Theory Series A 119 (2012) 382-396
  Joint with Imre Leader and Paul A. Russell
  DOI 10.1016/j.jcta.2011.09.005
  Journal Version. arXiv Local PDF.


• Transitive Sets and Cyclic Quadrilaterals
  Journal of Combinatorics 2 (2011) 457–462
  Joint with Imre Leader and Paul A. Russell
  Journal Version. arXiv Local PDF.


• Random Geometric Graphs (survey paper)
  Surveys in Combinatorics 2011. Edited by Robin Chapman. London Mathematical Society Lecture Note Series, 392. Cambridge University Press, Cambridge, 2011


• Lion and Man -- Can Both Win?
  Israel Journal of Mathematics 189 (2012) 267–286
  Joint with Béla Bollobás and Imre Leader
  DOI 10.1007/s11856-011-0158-6.
  Journal Version. Extended but older arXiv version:arXiv Local PDF PS.


• Hamilton Cycles in Random Geometric Graphs.
  Annals of Applied Probability 21 (2011) 1053-1072
  Joint with József Balogh, Béla Bollobás, Michael Krivelevich and Tobias Müller.
  DOI 10.1214/10-AAP718 Journal Copy Local PS , PDF


• Sentry selection in wireless networks.
  Advances in Applied Probability 42 (2010) 1-25
  Joint with Paul Balister, Béla Bollobás and Amites Sarkar.
  DOI 10.1239/aap/1269611141 Journal Copy PDF


• Random majority percolation.
  Random Structures and Algorithms 36 (2010), 315-340
  Joint with Paul Balister, Béla Bollobás and J. Robert Johnson.
  DOI 10.1002/rsa.20281 Journal Copy
  


• A critical constant for the k-nearest neighbour model.
  Advances in Applied Probability 41 (2009), 001-012
  Joint with Paul Balister, Béla Bollobás and Amites Sarkar.
  DOI 10.1239/aap/1240319574 Journal Copy arXiv Local PS PDF
  


• Random transceiver networks.
  Advances in Applied Probability 41 (2009), 323-343
  Joint with Paul Balister and Béla Bollobás.
  DOI 10.1239/aap/1246886613 Journal Copy Local PS
  


• Rectangles as sums of squares.
  Discrete Maths 309 (2009), 2913-2921
  DOI 10.1016/j.disc.2008.07.028 Journal Copy Local PS PDF


• Highly connected random geometric graphs.
  Discrete Applied Maths 157 (2009), 309-320
  Joint with Paul Balister, Béla Bollobás and Amites Sarkar.
  DOI 10.1016/j.dam.2008.03.001 Journal Copy . Local PS PDF
  


• Connectivity of a Gaussian Network.
  International Journal of Ad Hoc and Ubiquitous Computing 3 (2008) 204-213
  Joint with Paul Balister, Béla Bollobás and Amites Sarkar.
  DOI 10.1504/IJAHUC.2008.018407 Journal Copy . Local PDF


• Rigorous confidence intervals for critical probabilities.
  Phys. Rev. E 76 (2007) 011110 (8 pages)
  Joint with Oliver Riordan.
  DOI 10.1103/PhysRevE.76.011110 Journal Copy . ARXIV Local PS


• Extensions of the Polynomial Hales-Jewett Theorem.
  Combinatorics, Probability and Computing. 16 (2007) 789-803
  DOI 10.1017/S0963548306008339 Journal Copy . Local PS


• Connectivity of random k-nearest neighbour graphs.
  Adv. in Appl. Probability 37 (2005) 1-24.
  Joint with Paul Balister, Béla Bollobás and Amites Sarkar.
  DOI 10.1239/aap/1113402397. Journal Copy . Local PDF


• Continuum percolation with steps in the square or disc.
  Random Structures & Algorithms 26 (2005) 392-403
  Joint with Paul Balister and Béla Bollobás.
  DOI 10.1002/rsa.20064 Journal Copy . Local PS


• Fast transmission in ad hoc networks.
  Proceedings. IEEE International Symposium on Information Theory, 2004. Page 19
  Joint with Paul Balister, Béla Bollobás and Martin Haenggi.
  DOI 10.1109/ISIT.2004.1365055 Journal Copy .


• Continuum percolation with steps in an annulus.
  Ann. Appl. Probab. 14 (2004) 1869 - 1879.
  Joint with Paul Balister and Béla Bollobás.
  DOI 10.1214/105051604000000891 Journal Copy . Local PS


• Combinatorial Proofs of the Polynomial van der Waerden Theorem and the Polynomial Hales-Jewett Theorem.
  Journal of the London Mathematical Society. 61 (2000) 1-12
  DOI 10.1112/S0024610799008388 Journal Copy . Local PS

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