Results 11 to 20 of about 1,699 (154)
The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs [PDF]
Random Structures &Algorithms, Volume 66, Issue 2, March 2025., 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
semanticscholar +2 more sources
Rainbow Pancyclicity in Graph Systems [PDF]
The Electronic Journal of Combinatorics, 2019 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. a cycle with edge set $\{e_1,\ldots,e_n\}$ such that $e_i\in E(G_i)$ for $1\leq i \leq n$.
Yangyang Cheng, Guanghui Wang, Yi Zhao
semanticscholar +7 more sources
Pancyclicity of Hamiltonian graphs [PDF]
Journal of the European Mathematical Society, 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
Nemanja Draganić +2 more
openaire +3 more sources
Chvátal-Erdős condition for pancyclicity [PDF]
Journal of the Association for Mathematical Research, 2023 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. A celebrated meta-conjecture of Bondy states that every non-trivial condition implying Hamiltonicity also implies pancyclicity (up to possibly a few exceptional graphs).
Nemanja Draganić +2 more
semanticscholar +6 more sources
Two-Disjoint-Cycle-Cover Pancyclicity of Dragonfly Networks
MathematicsInterconnection networks (often modeled as graphs) are critical for high-performance computing systems, as they have significant impact on performance metrics like latency and bandwidth.
Zengxian Tian, Guanlin He
doaj +2 more sources
A generalization of Bondy’s pancyclicity theorem [PDF]
Combinatorics, probability & computing, 2023 The \emph{bipartite independence number} of a graph $G$, denoted as $\tilde\alpha(G)$, is the minimal number $k$ such that there exist positive integers $a$ and $b$ with $a+b=k+1$ with the property that for any two sets $A,B\subseteq V(G)$ with $A=a$ and
Nemanja Draganić +2 more
openalex +3 more sources
Pancyclicity in the Cartesian Product (K9 −C9)N [PDF]
Social Science Research Network, 2022 A graph G on m vertices is pancyclic if it contains cycles of length l , 3 ≤ l ≤ m as subgraphs in G . The complete graph K 9 on 9 vertices with a cycle C 9 of length 9 deleted from K 9 is denoted by ( K 9 − C 9 ).
Syeda Afiya, M. Rajesh
openalex +2 more sources
Toughness, Forbidden Subgraphs and Pancyclicity [PDF]
Graphs and Combinatorics, 2021 AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$
Wei Zheng, Hajo Broersma, Ligong Wang
openalex +3 more sources
Hamiltonicity and pancyclicity of superclasses of claw-free graphs
Filomat, 2023 A graph G is called to be fully cycle extendable graph [3] if each vertex of G belongs to a triangle and for any cycle C with |V(C)| < |V(G)| there exists a cycle C? in G such that V(C) ? V(C?) and |V(C?)| = |V(C)|+1. In this paper, we show that every
Abd‐El‐Kader Sahraoui +1 more
openalex +3 more sources
Discussiones Mathematicae Graph Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenming Bi, Ping Zhang
openalex +4 more sources