2018/01/02 by Dirk Meierling, Dieter Rautenbach, Meierling, Dirk +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1801.00726
arxiv created 2018/01/02 · arxiv updated 2018/01/03
We give short and simple proofs of the inequalities B(G)≤ Z(L(G)) and Z(G)≤ Z(L(G)) first established by Erzurumluoğlu, Meagher, and Pike, where G is a graph without isolated vertices, B(G) is the brushing number of G, Z(G) is the zero forcing number of G, and L(G) is the line graph of G.