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- W2009735547 abstract "We consider the d-dimensional grid graph $G=G_m^d$ on vertices ${1,2,ldots ,m}^d$ (a subset of ${bf Z}^d$), where two vertices are joined if and only if their coordinates differ in one place and have a difference of just 1. The graph is bipartite, and the $m^d$ vertices have bipartition W and B (sets W, B can be determined by the parity of their sum of coordinates). We show that there are constants $a_d,b_d$ so that for every even m, if we choose subsets $B'subseteq B$ and $W'subseteq W$ in the d-dimensional grid graph G, which satisfy the three conditions (i) $|B'|=|W'|$, (ii) for any $x,yin B'$, $d_G(x,y)ge a_dm^{1/d}+b_d$, and (iii) for any $x,yin W'$, $d_G(x,y)ge a_dm^{1/d}+b_d$, then G with the vertices $B'cup W'$ deleted has a perfect matching. The factor $m^{1/d}$ is best possible." @default.
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- W2009735547 date "2011-01-01" @default.
- W2009735547 modified "2023-09-25" @default.
- W2009735547 title "Perfect Matchings in Grid Graphs after Vertex Deletions" @default.
- W2009735547 doi "https://doi.org/10.1137/090776706" @default.
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