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- W1979462583 abstract "For a fixed tree T with n vertices the corresponding acyclic Birkhoff polytope Ωn(T) consists of doubly stochastic matrices having support in positions specified by T (matrices associated with T). The skeleton of Ωn(T) is the graph whose vertices are the permutation matrices associated with T and two vertices (permutation matrices) A and B are adjacent if and only if (E(GA)∖E(GB))∪(E(GB)∖E(GA)) is the edge set of a nontrivial path, where E(GA) and E(GB) are the edge sets of graphs associated with A and B, respectively. We present a formula to compute the degree of any vertex in the skeleton of Ωn(T). We also describe an algorithm for computing this number. In addition, we determine the maximum degree of a vertex in the skeleton of Ωn(T), for certain classes of trees, including paths and generalized stars where the branches have equal length." @default.
- W1979462583 created "2016-06-24" @default.
- W1979462583 creator A5001797411 @default.
- W1979462583 date "2015-06-01" @default.
- W1979462583 modified "2023-09-29" @default.
- W1979462583 title "Computing the degree of a vertex in the skeleton of acyclic Birkhoff polytopes" @default.
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- W1979462583 doi "https://doi.org/10.1016/j.laa.2015.02.005" @default.
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