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Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 03/2018, Volume 129, pp. 148 - 157
If a graph G is 3-connected and has minimum degree at least 4, then some longest cycle in G has a chord. If G is 2-connected and cubic, then every longest... 
Longest cycles | Chords | Connectivity | CIRCUITS | MATHEMATICS | 3-CONNECTED GRAPHS | INDEPENDENT DOMINATING SETS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 03/2018, Volume 87, Issue 3, pp. 374 - 393
In this article, we consider the following problem proposed by Locke and Zhang in 1991: Let G be a k‐connected graph with minimum degree d and X a set of m... 
minimum degree | k‐connected graph | longest cycle | k-connected graph
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 269 - 277
A planar 3-connected graph is called essentially 4-connected if, for every 3-separator , at least one of the two components of − is an isolated vertex. Jackson... 
05C10 | essentially 4-connected planar graph | shortness coefficient | 05C38 | circumference | longest cycle | MATHEMATICS | 05c10 | 05c38
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2019, Volume 258, pp. 87 - 96
We prove two sufficient conditions for Hamiltonian cycles in balanced bipartite digraphs. Let D be a strongly connected balanced bipartite digraph of order 2a.... 
Hamiltonian cycles | Bipartite digraphs | Longest non-Hamiltonian cycles | Perfect matching | PATHS | MATHEMATICS, APPLIED | Apexes | Graph theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2016, Volume 204, pp. 6 - 12
Although, the Hamiltonicity of solid grid graphs are polynomial-time decidable, the complexity of the longest cycle problem in these graphs is still open. In... 
Hamiltonian cycle | Approximation algorithm | Solid grid graph | Longest cycle | PATH | MATHEMATICS, APPLIED | Algorithms | Graphs | Approximation | Mathematical analysis | Images | Complexity
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 186, Issue 1, pp. 251 - 259
In 1978, C. Thomassen proved that in any graph one can destroy all the longest cycles by deleting at most one third of the vertices. We show that for graphs... 
Circumference | Vertex deletion | Longest cycle | MATHEMATICS, APPLIED
Journal Article
Electronic Journal of Graph Theory and Applications, ISSN 2338-2287, 10/2019, Volume 7, Issue 2, pp. 277 - 299
In this paper, we consider the least integer d such that every k -connected graph G of order n (and of independent number α ) has a longest cycle containing... 
longest cycle, connectivity, independent number, large degree vertex
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 11/2017, Volume 24, Issue 4
A well-known conjecture of Thomassen states that every cycle of maximum order in a 3-connected graph contains a chord. While many partial results towards this... 
Plane | Euclidean Ramsey theory | Combinatorial geometry | MATHEMATICS | Cycles | 3-CONNECTED GRAPHS | MATHEMATICS, APPLIED | Minimum degree | LONGEST CIRCUITS | Graph theory
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 7, pp. 1181 - 1184
Let G be any graph, and let c ( G ) denote the circumference of G . If, for every pair c 1 , c 2 of positive integers satisfying c 1 + c 2 = c ( G ) , the... 
Circumference | Partition | Dominating cycle | Path partition conjecture | Longest cycle | MATHEMATICS, APPLIED | CONNECTIVITY | RELATIVE LENGTH | PATH PARTITIONS | GRAPHS | Integers | Graphs | Partitions | Mathematical analysis | Circumferences
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 12/2019, Volume 62, Issue 4, pp. 879 - 911
We give algorithms with running time $$2^{\mathcal {O}({\sqrt{k}\log {k}})} \cdot n^{\mathcal {O}(1)}$$ 2 O ( k log k ) · n O ( 1 ) for the following problems.... 
68Q25 | Computational Mathematics and Numerical Analysis | 68W40 | Feedback vertex set | 68W01 | Mathematics | Longest cycle | Unit square graph | Longest path | Cycle packing | Combinatorics | Unit disk graph | Parameterized complexity | Theorems | Algorithms | Apexes | Run time (computers) | Graphs | Separators | Markov analysis
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2014, Volume 28, Issue 1, pp. 335 - 341
Let G be a graph of order n. Let lpt(G) be the minimum cardinality of a set X of vertices of G such that X intersects every longest path of G, and define... 
Transversal | Longest path | Longest cycle | transversal | MATHEMATICS, APPLIED | longest path | longest cycle | GRAPHS | Graphs | Upper bounds | Mathematical analysis | Austenitic stainless steels
Journal Article
Journal of Evolutionary Economics, ISSN 0936-9937, 12/2016, Volume 26, Issue 5, pp. 971 - 1006
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 07/2015, Volume 31, Issue 4, pp. 897 - 914
Let k >= 2be a positive integer and be a -connected graph. We prove that for any two cycles and in there exist two cycles and such that and . Moreover, we... 
Common vertices | k-connected graph | Longest cycle | MATHEMATICS | INDEPENDENCE NUMBER | LONGEST CYCLES
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2018, Volume 238, pp. 70 - 76
Let D be a strongly connected balanced bipartite directed graph of order 2a≥8. In this note we prove: (i). IfDcontains a cycle of... 
Cycles | Hamiltonian cycles | Longest non-Hamiltonian cycles | Bipartite balanced digraph | Even pancyclic | Digraphs | Pancyclic | MATHEMATICS, APPLIED | THEOREM | CYCLES | Cycles Hamiltonian cycles | GRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 24, pp. 6339 - 6347
Let G be any graph and let c ( G ) denote the circumference of G . We conjecture that for every pair c 1 , c 2 of positive integers satisfying c 1 + c 2 = c (... 
Circumference | Partition | Path partition conjecture | Longest cycle | MATHEMATICS | PATH PARTITIONS
Journal Article
The Journal of Supercomputing, ISSN 0920-8542, 4/2017, Volume 73, Issue 4, pp. 1322 - 1336
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 03/2019, Volume 35, Issue 2, pp. 479 - 483
We describe an infinite family of 2-connected graphs, each of which has the property that the intersection of all longest cycles is empty. In particular, we... 
Circumference | Vertex deletion | Longest cycle | MATHEMATICS | SUBGRAPH | Computer science | Graphs | Circumferences
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 537 - 549
Let D be a strongly connected directed graph of order n≥4. In Bang-Jensen et al. (1996), (J. of Graph Theory 22 (2) (1996) 181–187), J. Bang-Jensen, G. Gutin... 
Cycles | Hamiltonian cycles | Longest non-Hamiltonian cycles | Digraphs | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | THEOREM | GRAPHS
Journal Article
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