n-Hamiltonian graphs

Chartrand, Gary; Kapoor, Sanjiv; Lick, Don R.

doi:10.1016/s0021-9800(70)80069-2

Cited by 37 publications

(19 citation statements)

References 2 publications

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“…For instance, in Figure 1, the vertex x may be adjacent to more than one vertex in certain x-parts. Note that, since d&, yj) = (x,,x,') 5 3, and dG(y,,y,3 5 3, we have x,y,,x,x,',y,y,! E E(G3 -{x.Y}>.…”

Section: Domination In Graphs 741mentioning

confidence: 99%

The 2‐hamiltonian cubes of graphs

Koh

Teo

1989

Journal of Graph Theory

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This paper deals with the problem of characterizing the pairs of vertices x,y,in a connected graph G such that G3 -{x,y] is hamiltonian, where G IS the cube of G. It is known that the cube G is 2-hamiltonian if G is 2-connected. In this paper, w e first prove the stronger result that G3 -{x,y} is hamiltonian if either x or y is not a cut-vertex of G, and $en proceed to characterize those cut-vertices x and y of G such that G -(x,y) is hamiltonian. As a simple consequence of these, w e obtain Schaar's characterization of a connected graph G such that G3 is 2-hamiltonian.tween the vertices u and v in G. For any given positive integer k, the kth power of G, denoted by Gk, is the graph suchsthat V(Gk) = V(G) and E(Gk) = {uvIdc(u,v) 5 k}.

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Section: Domination In Graphs 741mentioning

confidence: 99%

The 2‐hamiltonian cubes of graphs

Koh

Teo

1989

Journal of Graph Theory

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“…A graph G is n-Hamiltonian if the removal of any set of n 2 0 points from G results in a Hamiltonian graph [2]. Note that if G is n-Hamiltonian, it is (n + 2)connected.…”

Section: N-hamiltonian Graphsmentioning

confidence: 99%

TOUGHNESS, HAMILTONIAN‐CONNECTEDNESS, AND n‐HAMILTONICITY

Molluzzo

1979

Annals of the New York Academy of Sciences

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“…Following [4] Suppose th e le mma is true for all trees T' with IV(T') I < q, and let T be a tree with q vertices which satisfies the conditions of the lemma. Let T " T2,.…”

Section: -Hamiltonian Powers Of Graphsmentioning

confidence: 99%

Some Hamiltonian results in powers of graphs

Hobbs¹

1973

J. RES. NATL. BUR. STAN. SECT. B. MATH. SCI.

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In this paper we show that the connectivity of the kth power of a graph of connectivity m is at least km if the kth power of the graph is not a complete graph. Also, we. prove th at removing as many as k -2 vertices from the kth power of a graph (k ;;. 3) leaves a Hamiltonian graph, and that removing as many as k -3 vertices from the kth power of a graph (k;;' 3) leaves a Hamiltonian con nected graph. Further, if every vertex of a graph has degree two or more, then the square of th e graph contai ns a 2-factor. Finally, we show that the squares of certain Euler graphs are Hamiltonian.

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n-Hamiltonian graphs

Cited by 37 publications

References 2 publications

The 2‐hamiltonian cubes of graphs

The 2‐hamiltonian cubes of graphs

TOUGHNESS, HAMILTONIAN‐CONNECTEDNESS, AND n‐HAMILTONICITY

Some Hamiltonian results in powers of graphs

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