Strong difference families over arbitrary graphs

2008 ◽  
Vol 16 (6) ◽  
pp. 443-461 ◽  
Author(s):  
Marco Buratti ◽  
Lucia Gionfriddo

2020 ◽  
Vol 343 (4) ◽  
pp. 111776 ◽  
Author(s):  
Yanxun Chang ◽  
Simone Costa ◽  
Tao Feng ◽  
Xiaomiao Wang




2018 ◽  
Vol 50 ◽  
pp. 391-405 ◽  
Author(s):  
Simone Costa ◽  
Tao Feng ◽  
Xiaomiao Wang




2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .



2019 ◽  
Vol 87 (11) ◽  
pp. 2461-2467 ◽  
Author(s):  
Marco Buratti ◽  
Dieter Jungnickel
Keyword(s):  


2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.



2013 ◽  
Vol 513 ◽  
pp. 38-52 ◽  
Author(s):  
Arash Farzan ◽  
J. Ian Munro
Keyword(s):  


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