A Sufficient Condition for an IC-Planar Graph to be Class 1

A Sufficient Condition for an IC-Planar Graph to be Class 1

Two distinct crossings are independent if the end-vertices of any two pairs of crossing edges are disjoint. A graph said to be plane graph with independent crossings or IC-planar, if it can be drawn in the plane such that every two crossings are independent. In this paper, we proved that every IC-pl...

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Veröffentlicht in:Graphs and combinatorics 2021-11, Vol.37 (6), p.2305-2313
Hauptverfasser: Duan, Yuanyuan, Song, Wenyao
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Combinatorics
Engineering Design
Graph coloring
Graph theory
Mathematics
Mathematics and Statistics
Original Paper
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Beschreibung
Zusammenfassung:Two distinct crossings are independent if the end-vertices of any two pairs of crossing edges are disjoint. A graph said to be plane graph with independent crossings or IC-planar, if it can be drawn in the plane such that every two crossings are independent. In this paper, we proved that every IC-planar graph G with Δ ( G ) = 7 admits a proper edge-coloring with Δ ( G ) colors if G does not contain a 6-cycle with three chords.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-021-02353-2