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Rotation numbers for unions of circuits
Author(s) -
Bollobás Béla,
Cockayne E. J.,
Yao Fang Zu
Publication year - 1984
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190080108
Subject(s) - combinatorics , mathematics , vertex (graph theory) , upper and lower bounds , graph , disjoint sets , undirected graph , simple graph , bound graph , rotation (mathematics) , discrete mathematics , graph power , line graph , geometry , mathematical analysis
Let G be a simple undirected graph which has p vertices and is rooted at x. Informally, the rotation number h(G, x) of this rooted graph is the minimum number of edges in a p ‐vertex graph F , such that for each vertex v of F , there exists a copy of G in F with the root x at v. In this paper, we calculate a lower bound for the rotation number of the graph which is the disjoint union of circuits C k , C e where 4 ⩽ k < ⩽, give infinite classes where this bound is exact, and obtain classes of rotation numbers for the case k = 4.