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571
Hamiltonian Cycles in Sparse Graphs
, 2004
"... The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle that pas ..."
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The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle
Computing the Toughness and the Scattering Number for Interval and Other Graphs
, 1994
"... We show that the scattering number and the toughness of a graph, two graph parameters strongly related to hamiltonian properties of graphs, can be computed in polynomial time on interval graphs, circulararc graphs, permutation graphs, circular permutation graphs, trapezoid graphs and cocomparabilit ..."
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We show that the scattering number and the toughness of a graph, two graph parameters strongly related to hamiltonian properties of graphs, can be computed in polynomial time on interval graphs, circulararc graphs, permutation graphs, circular permutation graphs, trapezoid graphs
Conditions for the existence of Hamiltonian circuits in graphs based on vertex degrees
 J. London Math. Soc
, 1985
"... The terminology used in this paper is that of [7]. The term graph denotes a finite, undirected graph without loops or multiple edges. For any vertex x e V of a graph G = (V, E) let N(x) be the set of vertices adjacent to x, and let d{x) be the degree of x. For any two nonadjacent vertices a and b w ..."
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Cited by 7 (0 self)
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The terminology used in this paper is that of [7]. The term graph denotes a finite, undirected graph without loops or multiple edges. For any vertex x e V of a graph G = (V, E) let N(x) be the set of vertices adjacent to x, and let d{x) be the degree of x. For any two nonadjacent vertices a and b
Toughness and longest cycles in . . .
, 1996
"... Let G be a planar graph on n vertices, let c(G) denote the length of a longest cycle of G, and let w(G) denote the number of components of G. By a wellknown theorem of Tutte, c(G) = n (i.e., G is hamiltonian) if G is 4connected. Recently, Jackson and Wormald showed that c(G) 2 ona for some positi ..."
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Let G be a planar graph on n vertices, let c(G) denote the length of a longest cycle of G, and let w(G) denote the number of components of G. By a wellknown theorem of Tutte, c(G) = n (i.e., G is hamiltonian) if G is 4connected. Recently, Jackson and Wormald showed that c(G) 2 ona for some
Advances on the Hamiltonian problem  A survey
, 2002
"... This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs. ..."
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Cited by 34 (0 self)
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This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs.
Updating the hamiltonian problem  a survey
 J. GRAPH THEORY
, 1991
"... This is intended as a survey article covering recent developments in the area of hamiltonian graphs, that is, graphs containing a spanning cycle. This article also contains some material on related topics such as traceable, hamiltonianconnected and pancyclic graphs and digraphs, as well as an exten ..."
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Cited by 25 (1 self)
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This is intended as a survey article covering recent developments in the area of hamiltonian graphs, that is, graphs containing a spanning cycle. This article also contains some material on related topics such as traceable, hamiltonianconnected and pancyclic graphs and digraphs, as well
Finding Hamiltonian Circuits in Arrangements of Jordan Curves is NPComplete
 Information Processing Letters 52
, 1994
"... Let A = fC 1 ; C 2 ; : : : ; C n g be an arrangement of Jordan curves in the plane lying in general position, i.e., every curve properly intersects at least one other curve, no two curves touch each other and no three meet at a common intersection point. The Jordancurve arrangement graph of A has as ..."
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Cited by 4 (0 self)
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whether Jordancurve arrangement graphs are Hamiltonian is NPcomplete. KEYWORDS NPcompleteness; Hamiltonian circuit; arrangements of Jordan curves; computational complexity; computational geometry 1 Introduction A Hamiltonian circuit in a graph is a circuit which passes through every vertex
Edmonds polytopes and a hierarchy of combinatorial problems
, 2006
"... Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality Σaj xj ≤ a0, where a1,a2,...,an are integ ..."
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Cited by 170 (0 self)
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that there is no upper bound on the rank of problems arising from the search for largest independent sets in graphs.
A filter for the circuit constraint
 Principles and Practice of Constraint Programming (CP 2006), Lecture Notes in Computer Science
, 2006
"... Abstract. We present an incomplete filtering algorithm for the circuit constraint. The filter removes redundant values by eliminating nonhamiltonian edges from the associated graph. We identify nonhamiltonian edges by analyzing a smaller graph with labeled edges that is defined on a separator of the ..."
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Cited by 10 (5 self)
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Abstract. We present an incomplete filtering algorithm for the circuit constraint. The filter removes redundant values by eliminating nonhamiltonian edges from the associated graph. We identify nonhamiltonian edges by analyzing a smaller graph with labeled edges that is defined on a separator
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