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Paths and cycles concerning independent edges
Graphs and Combinatorics, 1990A natural generalization of the concept of alternating path for a matching is that of an admissible path. An admissible path or cycle D in a graph G for a set L of pairwise independent edges is one in which, whenever \(e\in L\), D either contains e or touches no vertex of e.
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Restricted Hamiltonian Paths and Cycles
2009In this chapter we discuss results on hamiltonian paths and cycles with special properties. We start by studying hamiltonian paths with one or more end-vertices prescribed, that is, we study paths which start in a given vertex, paths which connect two prescribed vertices and, finally, paths which start and end in specified vertices.
Jørgen Bang-Jensen, Gregory Z. Gutin
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Paths, Cycles, and Connectivity
2017In this chapter, we study some important fundamental concepts of graph theory. In Section 3.1 we start with the definitions of walks, trails, paths, and cycles. The well-known Eulerian graphs and Hamiltonian graphs are studied in Sections 3.2 and 3.3, respectively.
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Optimal Identifying Codes in Cycles and Paths
Graphs and Combinatorics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junnila, Ville, Laihonen, Tero
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1997
A walk in a graph G is a finite sequence of vertices x 0, x 1, ..., x n and edges a 1, a 2, ..., a n of G: $${x_0},{a_1},{x_1},{a_2}, \ldots ,{a_n},{x_n},$$ where the endpoints of a i are x i−1 and x i for each i. A simple walk is a walk in which no edge is repeated.
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A walk in a graph G is a finite sequence of vertices x 0, x 1, ..., x n and edges a 1, a 2, ..., a n of G: $${x_0},{a_1},{x_1},{a_2}, \ldots ,{a_n},{x_n},$$ where the endpoints of a i are x i−1 and x i for each i. A simple walk is a walk in which no edge is repeated.
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Simple Paths and Cycles Avoiding Forbidden Paths
2017A graph with forbidden paths is a pair (G, F) where G is a graph and F is a subset of the set of paths in G. A simple path avoiding forbidden paths in (G, F) is a simple path in G such that each subpath is not in F. It is shown in [S. Szeider, Finding paths in graphs avoiding forbidden transitions, DAM 126] that the problem of deciding the existence of
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1998
Traditional network location theory is concerned with the optimal location of facilities which can be considered as single points (emergency medical service stations, switching centers in communication networks, bus stops, mail boxes, etc.) However, in many real problems the facility to be located is too large to be modeled as a point. Examples of such
Labbé, Martine +2 more
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Traditional network location theory is concerned with the optimal location of facilities which can be considered as single points (emergency medical service stations, switching centers in communication networks, bus stops, mail boxes, etc.) However, in many real problems the facility to be located is too large to be modeled as a point. Examples of such
Labbé, Martine +2 more
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Finding Paths and Cycles of Superpolylogarithmic Length
SIAM Journal on Computing, 2004Let $\ell$ be the number of edges in a longest cycle containing a given vertex $v$ in an undirected graph. We show how to find a cycle through $v$ of length $\exp(\Omega(\sqrt {\log \ell/\log\log \ell}))$ in polynomial time. This implies the same bound for the longest cycle, longest $vw$-path, and longest path.
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Long Paths and Cycles in Dynamical Graphs
Journal of Statistical Physics, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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