Minimum implicit degree condition restricted to claws for hamiltonian cycles

Xing Huang ()
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Xing Huang: Aviation Industry Group

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 6, 773-780

Abstract: Abstract Let id(v) denote the implicit degree of a vertex v in a graph G. We define G to be implicit 1-heavy (implicit 2-heavy) if at least one (two) of the end vertices of each induced claw has (have) implicit degree at least n/2. In this paper, we prove that: (a) Let G be a 2-connected graph of order n ≥ 3. If G is implicit 2-heavy and |N(u) ∩ N(v)| ≥ 2 for every pair of vertices u and v with d(u, v) = 2 and max{id(u), id(v)}

Keywords: Implicit degree; Hamilton cycle; Implicit 1-heavy (Implicit 2-heavy) (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0159-y

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