Rotation numbers for unions of circuits | Zendy

Bollobás Béla | Zendy; Cockayne E. J. | Zendy; Yao Fang Zu | Zendy

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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.

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