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Minimum Power Dominating Sets of Random Cubic Graphs
Author(s) -
Kang Liying,
Wormald Nicholas
Publication year - 2017
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22053
Subject(s) - mathematics , cubic graph , combinatorics , heuristics , random graph , independent set , dominating set , discrete mathematics , graph , line graph , mathematical optimization , voltage graph , vertex (graph theory)
We present two heuristics for finding a small power dominating set of cubic graphs. We analyze the performance of these heuristics on random cubic graphs using differential equations. In this way, we prove that the proportion of vertices in a minimum power dominating set of a random cubic graph is asymptotically almost surely at most 0.067801. We also provide a corresponding lower bound of 1 / 29.7 ≈ 0.03367 using known results on bisection width.