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Research

Publications: Dr Mark Walters

Ivan M-R, Leader I, Walters M ( 2022 ) . Constructible graphs and pursuit . Theoretical Computer Science vol. 930 , 196 - 208 .
Leader I, Letzter S, Narayanan B, Walters M ( 2019 ) . Product-free sets in the free semigroup . European Journal of Combinatorics vol. 83 , Article UNSP 103003 ,
Balister P, Bollobás B, Gunderson K, Leader I, Walters M ( 2018 ) . Random geometric graphs and isometries of normed spaces . Transactions of the American Mathematical Society vol. 370 , ( 10 ) 7361 - 7389 .
Balister P, Bollobas B, Haenggi M, Sarkar A, Walters M ( 2017 ) . Sentry selection in senso rnetworks: theory and algorithms . INTERNATIONAL JOURNAL OF SENSOR NETWORKS vol. 24 , ( 3 ) 139 - 148 .
JOHNSON JR, Leader I, Walters M ( 2017 ) . Transitive Avoidance Games . The Electronic Journal of Combinatorics
Balister PB, Bollobas B, Furedi Z, Leader I, WALTERS MJ ( 2016 ) . Subtended Angles . Israel Journal of Mathematics
Erde J, Walters M ( 2016 ) . An n-in-a-row type game . ELECTRONIC JOURNAL OF COMBINATORICS vol. 23 , ( 3 ) Article ARTN P3.7 ,
Russell PA, Walters M ( 2013 ) . Probably Intersecting Families are Not Nested . COMBINATORICS PROBABILITY & COMPUTING vol. 22 , ( 1 ) 146 - 160 .
Falgas-Ravry V, Walters M ( 2012 ) . SHARPNESS IN THE k-NEAREST-NEIGHBOURS RANDOM GEOMETRIC GRAPH MODEL . ADVANCES IN APPLIED PROBABILITY vol. 44 , ( 3 ) 617 - 634 .
Falgas-Ravry V, Walters M ( 2012 ) . Sharpness in the <span class="italic">k</span>-Nearest-Neighbours Random Geometric Graph Model . Advances in Applied Probability vol. 44 , ( 3 ) 617 - 634 .
Walters M ( 2012 ) . Small components in k-nearest neighbour graphs . DISCRETE APPLIED MATHEMATICS vol. 160 , ( 13-14 ) 2037 - 2047 .
Bollobas B, Leader I, Walters M ( 2012 ) . Lion and man-can both win? . ISRAEL JOURNAL OF MATHEMATICS vol. 189 , ( 1 ) 267 - 286 .
Leader I, Russell PA, Walters M ( 2012 ) . Transitive sets in Euclidean Ramsey theory . JOURNAL OF COMBINATORIAL THEORY SERIES A vol. 119 , ( 2 ) 382 - 396 .
Balogh J, Bollobas B, Krivelevich M, Muller T, Walters M ( 2011 ) . HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS . ANN APPL PROBAB vol. 21 , ( 3 ) 1053 - 1072 .
Leader I, Russell PA, Walters M ( 2011 ) . Transitive sets and cyclic quadrilaterals . Journal of Combinatorics vol. 2 , ( 3 ) 457 - 462 .
Balister P, Bollobas B, Johnson JR, Walters M ( 2010 ) . Random Majority Percolation . RANDOM STRUCT ALGOR vol. 36 , ( 3 ) 315 - 340 .
Balister P, Bollobas B, Sarkar A, Walters M ( 2010 ) . SENTRY SELECTION IN WIRELESS NETWORKS . ADV APPL PROBAB vol. 42 , ( 1 ) 1 - 25 .
Balister P, Bollobás B, Sarkar A, Walters M ( 2010 ) . Sentry Selection in Wireless Networks . Advances in Applied Probability vol. 42 , ( 1 ) 1 - 25 .
Balister P, Bollobas B, Walters M ( 2009 ) . RANDOM TRANSCEIVER NETWORKS . ADV APPL PROBAB vol. 41 , ( 2 ) 323 - 343 .
Balister P, Bollobás B, Walters M ( 2009 ) . Random transceiver networks . Advances in Applied Probability vol. 41 , ( 2 ) 323 - 343 .
Walters M ( 2009 ) . Rectangles as sums of squares . DISCRETE MATH vol. 309 , ( 9 ) 2913 - 2921 .
Balister P, Bollobas B, Sarkar A, Walters M ( 2009 ) . A CRITICAL CONSTANT FOR THE k-NEAREST-NEIGHBOUR MODEL . ADV APPL PROBAB vol. 41 , ( 1 ) 1 - 12 .
Balister P, Bollobás B, Sarkar A, Walters M ( 2009 ) . A critical constant for the <span class="italic">k</span> nearest-neighbour model . Advances in Applied Probability vol. 41 , ( 1 ) 1 - 12 .
Balister P, Bollobas B, Sarkar A, Walters M ( 2009 ) . Highly connected random geometric graphs . DISCRETE APPL MATH vol. 157 , ( 2 ) 309 - 320 .
Balister P, Bollobás B, Haenggi M, Sarkar A, Walters M ( 2008 ) . Sentry Selection in Sensor Networks: A Sufficient Condition for k Single Covers . Conference: 2008 IEEE International Zurich Seminar on Communications106 - 107 .
Balister P, Bollobas B, Sarkar A, Walters M ( 2008 ) . Connectivity of a Gaussian network . INT J AD HOC UBIQ CO vol. 3 , ( 3 ) 204 - 213 .
Walters M ( 2007 ) . Extensions of the polynomial Hales-Jewett theorem . COMB PROBAB COMPUT vol. 16 , ( 5 ) 789 - 803 .
Riordan O, Walters M ( 2007 ) . Rigorous confidence intervals for critical probabilities . PHYS REV E vol. 76 , ( 1 ) Article 011110 ,
Balister P, Bollobas B, Walters M ( 2005 ) . Continuum percolation with steps in the square or the disc . RANDOM STRUCT ALGOR vol. 26 , ( 4 ) 392 - 403 .
Balister P, Bollobás B, Sarkar A, Walters M ( 2005 ) . Connectivity of random <span class="italic">k</span>-nearest-neighbour graphs . Advances in Applied Probability vol. 37 , ( 1 ) 1 - 24 .
Balister P, Bollobas B, Sarkar A, Walters M ( 2005 ) . Connectivity of random k-nearest-neighbour graphs . ADV APPL PROBAB vol. 37 , ( 1 ) 1 - 24 .
WALTERS MJ, Bollobas B, Balister P ( 2004 ) . Continuum percolation with steps in an annulus . Annals of Applied Probability vol. 14 , 1869 - 1879 .