On cyclically 4-connected cubic graphs
AbstractA 3-connected cubic graph is cyclically 4-connected if it has at least [Formula: see text] vertices and when removal of a set of three edges results in a disconnected graph, only one component has cycles. By introducing the notion of cycle spread to quantify the distance between pairs of edg...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2333397 |
| Summary: | AbstractA 3-connected cubic graph is cyclically 4-connected if it has at least [Formula: see text] vertices and when removal of a set of three edges results in a disconnected graph, only one component has cycles. By introducing the notion of cycle spread to quantify the distance between pairs of edges, we get a new characterization of cyclically 4-connected graphs. Let [Formula: see text] and [Formula: see text] denote the ladder and Möbius ladder on [Formula: see text] vertices, respectively. We prove that a 3-connected cubic graph G is cyclically 4-connected if and only if G is either the Petersen graph, [Formula: see text] or [Formula: see text] for [Formula: see text], or G is obtained from [Formula: see text] or [Formula: see text] by bridging pairs of edges with cycle spread at least [Formula: see text]. The concept of cycle spread also naturally leads to methods for constructing cyclically k-connected cubic graphs from smaller ones, but for [Formula: see text] the method is not exhaustive. |
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| ISSN: | 0972-8600 2543-3474 |