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- W2922957428 abstract "We say a graph G is locally P if for each vertex v in G the open neighbourhood of v induces a graph with property P . The Hamilton Cycle Problem (HCP) is the problem of deciding whether a graph contains a Hamilton cycle. It is known that the HCP is NP-complete for locally traceable (LT) graphs with maximum degree 6. We extend that result to 1-tough graphs and to graphs with restricted degree sequences. If R is a set of nonnegative integers, we say a graph G is R -regular if the degrees of all the vertices in V ( G ) are elements of R . We show that the HCP is NP-complete for R -regular LT graphs if R is any set of natural numbers with m a x ( R ) ≥ 6 , with the possible exception of { 4 , 6 } and { 6 } . It is known that the HCP is NP-complete for LH graphs with maximum degree 10. We improve this result by showing that the HCP is NP-complete for 1-tough LH graphs with maximum degree 9 and for R -regular LH graphs if R is any set of natural numbers with min ( R ) = 3 and max ( R ) ∈ { 9 , 10 } , or if R is any set of natural numbers with max ( R ) ≥ 11 . Finally, we show that the HCP for k -connected LH graphs that are also locally ( k − 1 ) -connected is NP-complete for every k ≥ 3 ." @default.
- W2922957428 created "2019-04-01" @default.
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- W2922957428 date "2019-08-01" @default.
- W2922957428 modified "2023-09-27" @default.
- W2922957428 title "The Hamilton Cycle Problem for locally traceable and locally hamiltonian graphs" @default.
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- W2922957428 doi "https://doi.org/10.1016/j.dam.2019.02.046" @default.
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