Small Graph Instances with Hamiltonian Cycles
Paths and compatible hamiltonian cycles
... compatible Hamiltonian cycle, was disproved by Mareke Van Garderen, Wouter Meulemans, Bettina Speckmann and Csaba T´ oth [31] (Figure ...compatible Hamiltonian cycles that can be ...Gabriel ...
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A Study of Sufficient Conditions for Hamiltonian Cycles
... a graph has, the more likely it is that a Hamiltonian cycle will ...on Hamiltonian theory treat Ore’s Theorem as the main result that began much of the study of Hamiltonian graphs, and Dirac’s ...
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Second Hamiltonian Cycles in Claw-Free Graphs
... every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian ...claw-free Hamiltonian graphs with minimum degree at least 3 have a second ...
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Improving bounds on large instances of graph coloring
... efficient graph coloring algorithm that could process properly both small and large ...of graph. We also believe that the best way to tackle graph coloring in a general way is to use not only ...
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Reconfigurations of Combinatorial Problems: Graph Colouring and Hamiltonian Cycle
... hamiltonian cycles. Equally interesting is to work on a restricted class of instances of a reconfiguration problem and possibly find a polyno- mial algorithm or look at specific features of the ...
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A Distributed algorithm to find Hamiltonian cycles in Gnp random graphs
... with graph theoretic ...find Hamiltonian cycles in random geometric networks with edge faults, which can model sensor networks (see [9] and ...
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Graph Invariants and Large Cycles: A Survey
... a graph, respectively. Each vertex and edge in a graph can be interpreted as simple cycles of lengths 1 and 2, ...A graph G is hamiltonian if G contains a Hamilton cycle, that is, a ...
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Embedding Two Edge-Disjoint Hamiltonian Cycles and Two Equal Node-Disjoint Cycles into Twisted Cubes
... edge-disjoint Hamiltonian cycles in the n -dimensional twisted cube T Q n ...Two cycles in a graph are said to be equal and node- disjoint if they contain the same number of nodes, there is no ...
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A note on the number of edges in a Hamiltonian graph with no repeated cycle length
... Let G be a graph obtained by adding chords to a cycle of length n. Markstr¨ om asked for the maximum number of edges in G if there are no two cycles in G with the same length. A simple counting argument ...
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On planar regular graphs degree three without Hamiltonian cycles 1
... Let us consider planar embedding of the graph G (i.e. planar topological graph according Berge, depicting G ) with definite Hamiltonian cycle H in it. The edges not contained in H let us call the ...
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Enumeration of Basic Hamilton Cycles in the Mangoldt Graph
... into Graph Theory, which paved the way for the emergence of Arithmetic ...Mangoldt graph M n which is an arithmetic graph associated with the Mangoldt function (n), n ≥ 1, an ...the ...
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Extremal problems in disjoint cycles and graph saturation
... a result of Kierstead and Kostochka [22] in the case |G| = 3k. Theorem 1.2.21 ([22]). Let G be a graph with θ(G) ≤ 2k − 1. Then G has an equitable k-coloring. Our Theorem 1.2.17 characterizes the sharpness ...
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Rainbow numbers for small cycles
... An edge-colored graph is called rainbow if all of its edges have distinct colors. For two graphs G and H, the anti-Ramsey number ar(G, H), introduced by Erd˝os et al. [3], is the maximum number of colors in an ...
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Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices
... 1-Toughness and embeddability in the torus. Let G be any 4-connected graph on any surface F 2 with Euler characteristic χ ( F 2 ) 0. Then G must be 1-tough. (See [12] for the argument.) On the other hand, if we ...
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Weakly Supervised Acquisition of Labeled Class Instances using Graph Random Walks
... of instances, we chose 100 random instances from the A8 results to compare to the top 100 instances produced by ...a small increase from 87% to 89% for the class Book Publishers, to a ...
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Two Edge-Disjoint Hamiltonian Cycles and Two-Equal Path Partition in Augmented Cubes
... Edge-Disjoint Hamiltonian Cycles and Two-Equal Path Partition in Augmented Cubes Ruo-Wei Hung ‡§ and Chien-Chih Liao ‡ Abstract—The n-dimensional hypercube network Q n is one of the most popular ...
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Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system
... 17. Gavrilov, L, Iliev, ID: Complete hyperelliptic integrals of the first kind and their non-oscillation. Trans. Am. Math. Soc. 356, 1185-1207 (2004) 18. Wang, J, Xiao, D: On the number of limit cycles in ...
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Random matchings which induce Hamilton cycles, and hamiltonian decompositions of random regular graphs
... Hamilton cycles (with suitable restrictions on the prescribed set of ...d-regular graph for fixed even d ≥ 4 asymptotically almost surely decomposes into d/2 Hamilton ...regular graph into regular ...
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ERASMUS MUNDUS MASTER ALGANT UNIVERSITÀ DEGLI STUDI DI PADOVA HAMILTONIAN CYCLES
... the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate ...generating graph of a non-abelian simple group contains ...
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Small cycles in the Pancake graph
... for some 4 6 k 6 n, joined by external edges between these subgraphs. Hence, all 8–cycles of P n , n > 4, could be found recursively by considering 8–cycles within each P k , 4 6 k 6 n, consisting of ...
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