Results 11 to 20 of about 47,947 (303)
PATHS AND CYCLES IN COLORED GRAPHS [PDF]
Electronic Notes in Discrete Mathematics, 2001 Let G be an (edge-)colored graph. A path (cycle) is called monochromatic if all the edges of it have the same color, and is called heterochromatic if all the edges of it have different colors. In this note, some sufficient conditions for the existence of monochromatic and heterochromatic paths and cycles are obtained.
Xueliang Li 0001 +2 more
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Noncrossing Longest Paths and Cycles
Graphs and Combinatorics22 pages, 8 figures, GD ...
Aloupis, Greg +9 more
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The Optimal Rubbling Number of Paths, Cycles, and Grids
Complexity, 2021 A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the strict rubbling ...
Zheng-Jiang Xia, Zhen-Mu Hong
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Criticality indices of 2-rainbow domination of paths and cycles [PDF]
Opuscula Mathematica, 2016 A \(2\)-rainbow dominating function of a graph \(G\left(V(G),E(G)\right)\) is a function \(f\) that assigns to each vertex a set of colors chosen from the set \(\{1,2\}\) so that for each vertex with \(f(v)=\emptyset\) we have \({\textstyle\bigcup_{u\in ...
Ahmed Bouchou, Mostafa Blidia
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Characterization of signed paths and cycles admitting minus dominating function [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G=(V,E,\sigma)$ be a finite signed graph. A function $f: V \rightarrow\{-1,0,1\}$ is a minus dominating function (MDF) of $ G $ if $f(u)+\sum_{v \in N(u)} \sigma (uv)f(v)\geq 1 $ for all $ u\in V $. In this paper we characterize signed paths and
S.R. Shreyas, M. Joseph
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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 ...
Cartwright, Dorwin, Gleason, Terry C.
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On Hamiltonian Paths and Cycles in Sufficiently Large Distance Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Christian Löwenstein +2 more
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Optimal Identifying Codes in Cycles and Paths [PDF]
, 2022 The concept of identifying codes in a graph was introduced by Karpovsky et al. (in IEEE Trans Inf Theory 44(2):599-611, 1998). These codes have been studied in several types of graphs such as hypercubes, trees, the square grid, the triangular grid ...
Laihonen T, Junnila V
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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, Henry A. Kierstead
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