منابع مشابه
Hamiltonian paths in Cayley graphs
The classical Lovász conjecture says that every connected Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log2 |G|, such that the corresponding Cayley graph contains a Hamiltonian cycle. We also present an explicit construction...
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We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topolog...
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Motivated by multi-robot construction systems, we introduce the problem of finding squeeze-free Hamiltonian paths in grid graphs. A Hamiltonian path is squeeze-free if it does not pass between two previously visited vertices lying on opposite sides. We determine necessary and sufficient conditions for the existence of squeeze-free Hamiltonian paths in staircase grid graphs. Our proofs are const...
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Grid graphs are subgraphs of the infinite 2-dimensional integer grid. The Hamiltonian path problem for general grid graphs is a well-known NP-complete problem. In this paper, we present necessary and sufficient conditions for the existence of a Hamiltonian path between two given vertices in L−shaped grid graphs. We also show that a Hamiltonian path between two given vertices of a L−shaped grid ...
متن کاملHamiltonian Paths and Cycles in Planar Graphs
We examine the problem of counting the number of Hamiltonian paths and Hamiltonian cycles in outerplanar graphs and planar graphs, respectively. We give an O(nαn) upper bound and an Ω(αn) lower bound on the maximum number of Hamiltonian paths in an outerplanar graph with n vertices, where α ≈ 1.46557 is the unique real root of α = α + 1. For any positive integer n ≥ 6, we define an outerplanar ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1976
ISSN: 0095-8956
DOI: 10.1016/0095-8956(76)90030-7