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- W2006892215 abstract "A graph G is said to be hamiltonian path saturated (HPS for short), if G has no hamiltonian path but any addition of a new edge in G creates a hamiltonian path in G . It is known that an HPS graph of order n has size at most ( n - 1 2 ) and, for n ⩾ 6 , the only HPS graph of order n and size ( n - 1 2 ) is K n - 1 ∪ K 1 . Denote by sat ( n , HP ) the minimum size of an HPS graph of order n . We prove that sat ( n , HP ) ⩾ ⌊ ( 3 n - 1 ) / 2 ⌋ - 2 . Using some properties of Isaacs’ snarks we give, for every n ⩾ 54 , an HPS graph G n of order n and size ⌊ ( 3 n - 1 ) / 2 ⌋ . This proves sat ( n , HP ) ⩽ ⌊ ( 3 n - 1 ) / 2 ⌋ for n ⩾ 54 . We also consider m -path cover saturated graphs and P m -saturated graphs with small size." @default.
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- W2006892215 date "2006-06-01" @default.
- W2006892215 modified "2023-10-18" @default.
- W2006892215 title "Hamiltonian path saturated graphs with small size" @default.
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- W2006892215 doi "https://doi.org/10.1016/j.dam.2005.05.035" @default.
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