On vertex bisection width of random d-regular graphs

• Autores: Josep Díaz, Öznur Yaşar Diner, Maria Serna, Oriol Serra
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 116-122
• Idioma: inglés
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• Resumen

  • Vertex Bisection is a graph partitioning problem in which the aim is to find a bisectionthat minimizes the number of vertices in one partite set that has a neighbor in the otherset. Here we are interested in giving upper bounds on the vertex bisection width of randomd-regular graphs. Our approach is based on analyzing a greedy algorithm by using theDifferential Equations Method. In this way, we obtain the first known upper bounds for thevertex bisection width in random regular graphs. The results are compared with experimentalones and with lower bounds obtained by Kolesnik and Wormald (Lower Bounds for theIsoperimetric Numbers of Random Regular Graphs, SIAM J. on Disc. Math. 28(1), 553-575,2014) for this parameter.