On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918290426691584 |
|---|---|
| author | Weiß, Meike Akpanya, Reymond Niemeyer, Alice C. |
| author_facet | Weiß, Meike Akpanya, Reymond Niemeyer, Alice C. |
| contents | A circuit double cover of a bridgeless graph is a collection of even subgraphs such that every edge is contained in exactly two subgraphs of the given collection. Such a circuit double cover describes an embedding of the corresponding graph onto a surface. In this paper, we investigate the well-known Orientable Strong Embedding Conjecture. This conjecture proposes that every bridgeless graph has a circuit double cover describing an embedding on an orientable surface. In a recent paper, we have proved that a 3-connected cubic planar graph G has exactly one orientable circuit double cover if and only if G is the dual graph of an Apollonian network. In this paper, we extend this result by demonstrating that this characterisation applies to any 3-connected planar graph, regardless of whether it is cubic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers Weiß, Meike Akpanya, Reymond Niemeyer, Alice C. Combinatorics Discrete Mathematics A circuit double cover of a bridgeless graph is a collection of even subgraphs such that every edge is contained in exactly two subgraphs of the given collection. Such a circuit double cover describes an embedding of the corresponding graph onto a surface. In this paper, we investigate the well-known Orientable Strong Embedding Conjecture. This conjecture proposes that every bridgeless graph has a circuit double cover describing an embedding on an orientable surface. In a recent paper, we have proved that a 3-connected cubic planar graph G has exactly one orientable circuit double cover if and only if G is the dual graph of an Apollonian network. In this paper, we extend this result by demonstrating that this characterisation applies to any 3-connected planar graph, regardless of whether it is cubic. |
| title | On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2601.10171 |