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Journal of Graph Theory, ISSN 0364-9024, 03/2020, Volume 93, Issue 3, pp. 350 - 362
We say that two graphs H1,H2 on the same vertex set are G‐creating if the union of the two graphs contains G as a subgraph. Let H(n,k) be the maximum number of... 
union | permutations | Hamiltonian path | even cycle
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2018, Volume 341, Issue 3, pp. 606 - 626
Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a... 
[formula omitted]-join | Graph factor | Hamiltonian cycle problem | T-join | MATHEMATICS | COMBINATORIAL OPTIMIZATION | DISJOINT SPANNING-TREES | GRAPHS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2020, Volume 89, Issue 322, pp. 965 - 991
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number k \ge 0 of hamiltonian cycles, which is especially... 
exhaustive generation | Bondy-Jackson conjecture | FAST GENERATION | MATHEMATICS, APPLIED | uniquely hamiltonian | INDEPENDENT DOMINATING SETS | Hamiltonian cycle | girth | cubic graph | uniquely traceable
Journal Article
Algorithms, ISSN 1999-4893, 09/2018, Volume 11, Issue 9, p. 140
The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C... 
Bipartite permutation graphs | Split graphs | Combinatorial reconfiguration | Chordal bipartite graphs | Hamiltonian cycle | PSPACE-complete | Strongly chordal graphs | Unit interval graphs | chordal bipartite graphs | unit interval graphs | split graphs | combinatorial reconfiguration | strongly chordal graphs | bipartite permutation graphs
Journal Article
Journal of Experimental Algorithmics (JEA), ISSN 1084-6654, 12/2019, Volume 24, Issue 1, pp. 1 - 18
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics.... 
Hamiltonian cycle | Bounded treewidth | experimental evaluation
Journal Article
IEICE Transactions on Information and Systems, ISSN 0916-8532, 2018, Volume E101.D, Issue 12, pp. 2916 - 2921
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2017, Volume 31, Issue 4, pp. 2328 - 2347
We prove that for all k >= 4 and 1 <= l < k/2, every k-uniform hypergraph H on n vertices with delta(k-2)(H) >= (4(k-l)-1/4(k-l)(2) + o(1)) ((n)(2)) contains a... 
Hamiltonian cycles | Hypergraphs | Degree conditions | DIRAC-TYPE THEOREM | MATHEMATICS, APPLIED | 3-UNIFORM HYPERGRAPHS | THRESHOLD | K-UNIFORM HYPERGRAPHS | hypergraphs | degree conditions | Mathematics - Combinatorics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2016, Volume 205, pp. 16 - 26
Let P be a graph property. A graph G is said to be locallyP if the subgraph induced by the open neighbourhood of every vertex in G has property P. Ryjáček’s... 
Fully cycle extendable | Weakly pancyclic | Hamiltonian | Locally isometric | Graphs | Extensibility | Polypropylenes | Mathematical analysis | Structural analysis
Journal Article
ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 01/2019, Volume 15, Issue 1, pp. 1 - 27
M AX -C UT , E DGE D OMINATING S ET , G RAPH C OLORING , and H AMILTONIAN C YCLE on graphs of bounded clique-width have received significant attention as they... 
Coloring | fine-grained complexity | Hamiltonian cycle | exponential time hypothesis | MATHEMATICS, APPLIED | ALGORITHMS | MINORS | DECOMPOSITIONS | LOWER BOUNDS | COMPLEXITY | PARTITIONING PROBLEMS | MONADIC 2ND-ORDER LOGIC | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 03/2020, Volume 56, Issue 2, pp. 339 - 372
We show that every 3‐uniform hypergraph H = (V,E) with |V(H)| = n and minimum pair degree at least (4/5 + o(1))n contains a squared Hamiltonian cycle. This may... 
Hamiltonian cycles | hypergraphs | Pósa's conjecture | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Posa's conjecture | Graphs | Graph theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2019, Volume 271, pp. 1 - 14
The pancake graph Pn is the Cayley graph of the symmetric group Sn on n elements generated by prefix reversals. Pn has been shown to have properties that makes... 
Cayley graphs | Weakly pancyclic | Burnt pancake graph | Hamiltonian cycles | MATHEMATICS, APPLIED | INTERCONNECTION NETWORKS | Permutations | Generators | Canonical forms | Group theory
Journal Article
IEEE Transactions on Parallel and Distributed Systems, ISSN 1045-9219, 02/2015, Volume 26, Issue 2, pp. 434 - 443
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 12/2012, Volume 22, Issue 12, pp. 1250296 - 1250230
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 07/2020, Volume 94, Issue 3, pp. 349 - 363
A graph is called 2 K 2‐free if it does not contain two independent edges as an induced subgraph. Broersma, Patel, and Pyatkin showed that every 25‐tough 2 K... 
Hamiltonian cycle | toughness | 2‐factor | 2K2‐free graph
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2013, Volume 161, Issue 18, pp. 2992 - 3004
A graph G is spanning r-cyclable of order t if for any r nonempty mutually disjoint vertex subsets A1,A2,…,Ar of G with |A1∪A2∪⋯∪Ar|≤t, there exist r disjoint... 
Cyclable | Graph | Hamiltonian cycle | Spanning cycle | Hypercube | MATHEMATICS, APPLIED | HAMILTONIAN DECOMPOSITIONS | SUPER LACEABILITY | CAYLEY-GRAPHS | Mathematical analysis | Graphs | Hypercubes
Journal Article
Optik, ISSN 0030-4026, 10/2016, Volume 127, Issue 20, pp. 8461 - 8468
P system is a new kind of distributed parallel computing model. In the P system, objects in each membrane can follow the evolution of the maximum parallelism... 
Membrane computing | Hamiltonian cycle problem | Natural computing | P system | SAT | OPTICS | MEMBRANE-INSPIRED ALGORITHM | Computer science | Analysis
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 1/2019, Volume 229, Issue 1, pp. 269 - 285
We prove that if an n-vertex graph with minimum degree at least 3 contains a Hamiltonian cycle, then it contains another cycle of length n−o(n); in particular,... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | INDEPENDENT DOMINATING SETS | COMPLEXITY | Graph theory | Research | Hamiltonian function | Mathematical research
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 2019
Let G=Cn1□Cn2□⋯□Cnk be a Cartesian product of k≥2 directed cycles. It is known that G has a Hamilton cycle if there is a permutation (n1′,n2′,…,nk′) of... 
Hamilton cycle | Cartesian product of directed cycles | Hamiltonian digraph | Hamiltonian decomposition
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 28 - 60
In a recent paper, we have studied the enumeration of Hamiltonian cycles (abbreviated HCs) on the grid cylinder graph × , where grows while is fixed. In this... 
Integers | Equivalence relation | Generating function | Plant roots | Mathematical lattices | Mathematics | Recurrence relations | Cylindrical surfaces | Cylinders | Vertices | MATHEMATICS | MATHEMATICS, APPLIED | WALKS | Hamiltonian cycles | Transfer matrix method | generating functions | thick grid cylinder | TRANSFER-MATRIX METHOD
Journal Article
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