[PDF][PDF] Hamiltonicity of cubic 3-connected k-Halin graphs
S Malik, AM Qureshi, T Zamfirescu - the electronic journal of combinatorics, 2013 - emis.de
S Malik, AM Qureshi, T Zamfirescu
the electronic journal of combinatorics, 2013•emis.deWe investigate here how far we can extend the notion of a Halin graph such that
hamiltonicity is preserved. Let $ H= T\cup C $ be a Halin graph, $ T $ being a tree and $ C $
the outer cycle. A $ k $-Halin graph $ G $ can be obtained from $ H $ by adding edges while
keeping planarity, joining vertices of $ HC $, such that $ GC $ has at most $ k $ cycles. We
prove that, in the class of cubic $3 $-connected graphs, all $14 $-Halin graphs are
hamiltonian and all $7 $-Halin graphs are $1 $-edge hamiltonian. These results are best …
hamiltonicity is preserved. Let $ H= T\cup C $ be a Halin graph, $ T $ being a tree and $ C $
the outer cycle. A $ k $-Halin graph $ G $ can be obtained from $ H $ by adding edges while
keeping planarity, joining vertices of $ HC $, such that $ GC $ has at most $ k $ cycles. We
prove that, in the class of cubic $3 $-connected graphs, all $14 $-Halin graphs are
hamiltonian and all $7 $-Halin graphs are $1 $-edge hamiltonian. These results are best …
Abstract
We investigate here how far we can extend the notion of a Halin graph such that hamiltonicity is preserved. Let be a Halin graph, being a tree and the outer cycle. A -Halin graph can be obtained from by adding edges while keeping planarity, joining vertices of , such that has at most cycles. We prove that, in the class of cubic -connected graphs, all -Halin graphs are hamiltonian and all -Halin graphs are -edge hamiltonian. These results are best possible.
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