Results 1 to 10 of about 1,711 (113)
Spectral Conditions of Pancyclicity For T-Tough Graphs [PDF]
arXiv.orgMore than 40 years ago Chv\'atal introduced a new graph invariant, which he called graph toughness. From then on a lot of research has been conducted, mainly related to the relationship between toughness conditions and the existence of cyclic structures,
Vladimir Benediktovich
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Rainbow vertex pair-pancyclicity of strongly edge-colored graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$.
Peixue Zhao, Fei Huang
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Chvátal-Erdős condition for pancyclicity [PDF]
European Conference on Combinatorics, Graph Theory and Applications, 2023 An $n$-vertex graph is \emph{Hamiltonian} if it contains a cycle that covers all of its vertices and it is \emph{pancyclic} if it contains cycles of all lengths from $3$ up to $n$.
Nemanja Draganić +2 more
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Pancyclicity of Hamiltonian graphs [PDF]
Journal of the European Mathematical Society (Print), 2022 An n -vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is pancyclic if it contains cycles of all lengths from 3 up to n .
Nemanja Draganić +2 more
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The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs [PDF]
Random Struct. Algorithms, 2023 Let μ(G)$$ \mu (G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a Hamiltonian graph, and let μ^(G)$$ \hat{\mu}(G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a pancyclic graph.
Yahav Alon, Michael Anastos
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Hamiltonicity, independence number, and pancyclicity [PDF]
, 2012 A graph on n vertices is called pancyclic if it contains a cycle of length l for all 3 \le l \le n. In 1972, Erdos proved that if G is a Hamiltonian graph on n > 4k^4 vertices with independence number k, then G is pancyclic.
Choongbum Lee, Benny Sudakov
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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
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A new approach to pancyclicity of Paley graphs I
, 2023 Let $G$ be an undirected graph of order $n$ and let $C_i$ be an $i$-cycle graph. $G$ is called pancyclic if $G$ contains a $C_i$ for any $i\in \{3,4,\ldots,n\}$.
Yusaku Nishimura
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Hamiltonicity, pancyclicity, and full cycle extendability in multipartite tournaments [PDF]
Journal of Graph Theory, 2020 A digraph D with n vertices is Hamiltonian (pancyclic and vertex‐pancyclic, respectively) if D contains a Hamilton cycle (a cycle of every length 3 , 4 , … , n , for every vertex v ∈ V ( D ) , a cycle of every length 3 , 4 , … , n through v ...
Zan-Bo Zhang +3 more
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Rainbow Pancyclicity in Graph Systems [PDF]
Electronic Journal of Combinatorics, 2021 Let $G_1,\ldots,G_n$ be graphs on the same vertex set of size $n$, each graph with minimum degree $\delta(G_i)\ge n/2$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e.
Yangyang Cheng, Guanghui Wang, Yi Zhao
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