Results 21 to 30 of about 395,936 (323)
Path Separation by Short Cycles [PDF]
Journal of Graph Theory, 2016 AbstractTwo Hamilton paths in are separated by a cycle of length k if their union contains such a cycle. For we bound the asymptotics of the maximum cardinality of a family of Hamilton paths in such that any pair of paths in the family is separated by a cycle of length k. We also deal with related problems, including directed Hamilton paths.
Cohen, Gérard +2 more
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The Number of Paths and Cycles in a Digraph [PDF]
Psychometrika, 1966 An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simple n-sequences. In this matrix, the i, j entry, i ≠j, gives the number of paths of length n from a point vi to a point vj; the diagonal entry i, i gives the number of cycles of length n containing vi.
Cartwright, Dorwin, Gleason, Terry C.
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Paths and cycles in tournaments [PDF]
Transactions of the American Mathematical Society, 1986 Sufficient conditions are given for the existence of an oriented path with given end vertices in a tournament. As a consequence a conjecture of Rosenfeld is established. This states that if n n is large enough, then every non-strongly oriented cycle of order n n is contained in every tournament of order n
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The Square of Paths and Cycles
Journal of Combinatorial Theory, Series B, 1995 The square of a cycle (path) is the graph obtained by joining every pair of vertices of distance two in the cycle (path). Posa conjectured that if a graph \(G\) on \(n\) vertices has minimum degree \(\delta(G)\) at least \({2\over 3}n\), then \(G\) contains the square of a Hamiltonian cycle.
Genghua Fan, Hal A. Kierstead
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Intersecting longest paths and longest cycles: A survey
Electronic Journal of Graph Theory and Applications, 2013 This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention.
Ayesha Shabbir +2 more
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Connected domination game played on Cartesian products
Open Mathematics, 2019 The connected domination game on a graph G is played by Dominator and Staller according to the rules of the standard domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of G. If
Bujtás Csilla +3 more
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Decomposition of hypercube graphs into paths and cycles of length four
AKCE International Journal of Graphs and Combinatorics, 2022 By a [Formula: see text]-decomposition of a graph G, we mean a partition of the edge set of G into p paths of length 4 and q cycles of length 4. In this paper, we give conditions for a [Formula: see text]-decomposition of the n-dimensional hypercube ...
D. Saranya, S. Jeevadoss
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Finding $k$ Simple Shortest Paths and Cycles [PDF]
, 2016 The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single source-sink pair,
Agarwal, Udit, Ramachandran, Vijaya
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On the radio number for corona of paths and cycles
AKCE International Journal of Graphs and Combinatorics, 2020 Radio -coloring of graphs is one of the variations of frequency assignment problem. For a simple connected graph and a positive integer , a radio -coloring is an assignment of positive integers (colors) to the vertices of such that for every pair of ...
Niranjan P.K., Srinivasa Rao Kola
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Embedding complete multi-partite graphs into Cartesian product of paths and cycles
Electronic Journal of Graph Theory and Applications, 2021 Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion, and the wirelength.
R. Sundara Rajan +4 more
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