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Properly colored paths and cycles
Discrete Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fujita, Shinya, Magnant, Colton
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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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Broadcasts on paths and cycles
Discrete Applied Mathematics, 2020 A broadcast on a graph $G=(V,E)$ is a function $f: V\longrightarrow \{0,\ldots,\operatorname{diam}(G)\}$ such that $f(v)\leq e\_G(v)$ for every vertex $v\in V$, where$\operatorname{diam}(G)$ denotes the diameter of $G$ and $e\_G(v)$ the eccentricity of $v$ in $G$.
Sabrina Bouchouika +2 more
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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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Multicluster interleaving on paths and cycles [PDF]
, 2005 Interleaving codewords is an important method not only for combatting burst errors, but also for distributed data retrieval. This paper introduces the concept of multicluster interleaving (MCI), a generalization of traditional interleaving problems.
Bruck, Jehoshua, Jiang, Anxiao (Andrew)
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Heavy and Light Paths and Hamilton Cycles
SSRN Electronic Journal, 2022 Given a graph $G$, we denote by $f(G,u_0,k)$ the number of paths of length $k$ in $G$ starting from $u_0$. In graphs of maximum degree 3, with edge weights $i.i.d.$ with $exp(1)$, we provide a simple proof showing that (under the assumption that $f(G,u_0,k)=ω(1)$) the expected weight of the heaviest path of length $k$ in $G$ starting from $u_0$ is at ...
Sahar Diskin, Dor Elboim
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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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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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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.
Li, Xueliang +2 more
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