Hamilton cycles in sparse locally connected graphs
A graph G is locally connected if for every v∈V(G) the open neighbourhood N(v) of v is nonempty and induces a connected graph in G. We characterize locally connected graphs of order n with less than 2n edges and show that for any natural number k the Hamilton Cycle Problem for locally connected grap...
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| Veröffentlicht in: | Discrete Applied Mathematics 2019-03, Vol.257, p.276-288 |
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| container_title | Discrete Applied Mathematics |
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| creator | van Aardt, Susan A. Burger, Alewyn P. Frick, Marietjie Thomassen, Carsten de Wet, Johan P. |
| description | A graph G is locally connected if for every v∈V(G) the open neighbourhood N(v) of v is nonempty and induces a connected graph in G. We characterize locally connected graphs of order n with less than 2n edges and show that for any natural number k the Hamilton Cycle Problem for locally connected graphs of order n with m edges is polynomially solvable if m≤2n+klog2n, but NP-complete if m=2n+⌊n1∕k⌋. |
| doi_str_mv | 10.1016/j.dam.2018.10.031 |
| format | Article |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Graphs Hamiltonian Locally connected NP-complete Polynomial time algorithm |
| title | Hamilton cycles in sparse locally connected graphs |
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