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2017 The $H$-linked degree-sum parameter for special graph families
Lydia East Kenney, Jeffrey Powell
Involve 10(4): 707-720 (2017). DOI: 10.2140/involve.2017.10.707

Abstract

For a fixed graph H, a graph G is H-linked if any injection f : V (H) V (G) can be extended to an H-subdivision in G. The concept of H-linked generalizes several well-known graph theory concepts such as k-connected, k-linked, and k-ordered. In 2012, Ferrara et al. proved a sharp σ2 (or degree-sum) bound for a graph to be H-linked. In particular, they proved that any graph G with n > 20|E(H)| vertices and σ2(G) n + a(H) 2 is H-linked, where a(H) is a parameter maximized over certain partitions of V (H). However, they do not discuss the calculation of a(H) in their work. In this paper, we prove the exact value of a(H) in the cases when H is a path, a cycle, a union of stars, a complete graph, and a complete bipartite graph. Several of these results lead to new degree-sum conditions for particular graph classes while others provide alternate proofs of previously known degree-sum conditions.

Citation

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Lydia East Kenney. Jeffrey Powell. "The $H$-linked degree-sum parameter for special graph families." Involve 10 (4) 707 - 720, 2017. https://doi.org/10.2140/involve.2017.10.707

Information

Received: 5 May 2016; Revised: 1 July 2016; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1359.05063
MathSciNet: MR3630312
Digital Object Identifier: 10.2140/involve.2017.10.707

Subjects:
Primary: 05C35, 05C38
Secondary: 05C83

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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