Abstract
Let G be a graph withE(G) $#x2260;ø. The line graph of G, written L(G) hasE(G) as its vertex set, where two vertices are adjacent in L(G) if and only if the corresponding edges are adjacent inG. Thomassen conjectured that all 4-connected line graphs are hamiltonian [2]. We show that this conjecture holds for planar graphs.
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Partially supported by NSA grant MDA904-94-H-2012
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Lai, HJ. Every 4-Connected Line Graph of a Planar Graph is Hamiltonian. Graphs and Combinatorics 10, 249–253 (1994). https://doi.org/10.1007/BF02986673
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DOI: https://doi.org/10.1007/BF02986673