2009/09/29 by Cheng Yeaw Ku, Ku, Cheng Yeaw, Kok Bin Wong +1 · 1 citation
Mathematics · #05C31 #05C70 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C31 #msc:05C70
paper · pdf · doi:10.48550/arxiv.0909.5249
arxiv created 2009/09/29 · arxiv updated 2009/12/01
In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define θ-barrier sets. Our definition of a θ-barrier set is slightly different from that of a barrier set. However we show that θ-barrier sets and barrier sets have similar properties. In particular, we prove a generalized Berge's Formula and give a characterization for the set of all θ-special vertices in a graph.