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- W1676015564 abstract "The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of degree partitions (respectively, degree sequences) of all simple graphs on the vertex set $[n]$. The polytope of degree sequences has been very well studied. In this paper we study the polytope of degree partitions. We show that adding the inequalities $x_1geq x_2 geq cdots geq x_n$ to a linear inequality description of the degree sequence polytope yields a linear inequality description of the degree partition polytope and we show that the extreme points of the degree partition polytope are the $2^{n-1}$ threshold partitions (these are precisely those extreme points of the degree sequence polytope that have weakly decreasing coordinates). We also show that the degree partition polytope has $2^{n-2}(2n-3)$ edges and $(n^2 -3n + 12)/2$ facets, for $ngeq 4$. Our main tool is an averaging transformation on real sequences defined by repeatedly averaging over the ascending runs." @default.
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- W1676015564 date "2006-05-05" @default.
- W1676015564 modified "2023-10-01" @default.
- W1676015564 title "The Polytope of Degree Partitions" @default.
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- W1676015564 doi "https://doi.org/10.37236/1072" @default.
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