Lancaster EPrints

An inductive construction of (2,1)-tight graphs

Nixon, Anthony and Owen, John (2014) An inductive construction of (2,1)-tight graphs. Contributions to Discrete Mathematics, 9 (2). pp. 1-16. ISSN 1715-0868

[img]
Preview
PDF (NixonOwen(2,1)Final) - Submitted Version
Available under License ["licenses_description_creative_commons_attribution_4_0_international_license" not defined].

Download (298Kb) | Preview

    Abstract

    The graphs $G=(V,E)$ with $|E|=2|V|-\ell$ that satisfy $|E'|\leq 2|V'|-\ell$ for any subgraph $G'=(V',E')$ (and for $\ell=1,2,3$) are the $(2,\ell)$-tight graphs. The Henneberg--Laman theorem characterizes $(2,3)$-tight graphs inductively in terms of two simple moves, known as the Henneberg moves. Recently, this has been extended, via the addition of a graph extension move, to the case of $(2,2)$-tight simple graphs. Here an alternative characterization is provided by means of vertex-to-$K_4$ and edge-to-$K_3$ moves. This is extended to the $(2,1)$-tight simple graphs by the addition of an edge joining move.

    Item Type: Article
    Journal or Publication Title: Contributions to Discrete Mathematics
    Subjects:
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 73134
    Deposited By: ep_importer_pure
    Deposited On: 03 Mar 2015 11:04
    Refereed?: Yes
    Published?: Published
    Last Modified: 28 Oct 2017 00:04
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/73134

    Actions (login required)

    View Item