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Sequences of Maximal Degree Vertices in Graphs

Khadzhiivanov, NickolayNenov, Nedyalko — 2004

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05C35. Let Γ(M ) where M ⊂ V (G) be the set of all vertices of the graph G adjacent to any vertex of M. If v1, . . . , vr is a vertex sequence in G such that Γ(v1, . . . , vr ) = ∅ and vi is a maximal degree vertex in Γ(v1, . . . , vi−1), we prove that e(G) ≤ e(K(p1, . . . , pr)) where K(p1, . . . , pr ) is the complete r-partite graph with pi = |Γ(v1, . . . , vi−1) Γ(vi )|.

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