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Adjacency Relationships Forced by a Degree Sequence [PDF]

open access: yesGraphs and Combinatorics, 2018
There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are not.
Michael D Barrus
exaly   +2 more sources

Convexity of degree sequences

Journal of Graph Theory, 1999
Summary: We explore the convexity of the set of vectors consisting of degree sequences of subgraphs of a given graph. Results of \textit{P. Katerinis} [J. Graph Theory 9, No. 4, 513-521 (1985; Zbl 0664.05047)] and \textit{P. Fraisse}, \textit{P. Hell} and \textit{D. G. Kirkpatrick} [Graphs Comb.
Richard P. Anstee, Yunsun Nam
openaire   +3 more sources

Descending sequences of degrees

Journal of Symbolic Logic, 1975
Our unexplained notation is that of Rogers [4]. Let P ⊆ 2N × 2N. We call a sequence <An: n ∈ N> of subsets of N a P-sequence iff ∀n(An+1 = the unique B such that P(An, B)).Theorem. Let P ⊆ 2N × 2N be arithmetical. Then there is no P-sequence <An: n ∈ N> such that ∀n(A′n+1 ≤T An).This theorem improves a result of Friedman [2] who showed that
openaire   +3 more sources

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