On finding hamiltonian cycles in Barnette graphs
Behrooz Bagheri Gh., Tomas Feder, Herbert Fleischner, Carlos Subi
TL;DR
This paper investigates Hamiltonian cycles in Barnette graphs, exploring the relationship with facial 2-factors, and establishes NP-completeness results related to Barnette's Conjecture and hamiltonicity.
Contribution
It introduces a new approach using (quasi) spanning trees of faces in G/Q and links the conjecture's falsity to NP-completeness of Hamiltonicity in certain graphs.
Findings
Hamiltonicity in certain planar cubic graphs relates to facial 2-factors.
If Barnette's Conjecture is false, Hamiltonian cycle detection becomes NP-complete.
Algorithmic complexity of finding spanning trees of faces is studied.
Abstract
In this paper, we deal with hamiltonicity in planar cubic graphs G having a facial 2-factor Q via (quasi) spanning trees of faces in G/Q and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette's Conjecture is false, then hamiltonicity in 3-connected planar cubic bipartite graphs is an NP-complete problem.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Limits and Structures in Graph Theory