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Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 10/2016, Volume 54, pp. 127 - 132
A graph G is hypohamiltonian/hypotraceable if it is not hamiltonian/traceable, but all vertex deleted subgraphs of G are hamiltonian/traceable. Until now all... 
hypotraceable graph | almost hypohamiltonian graph | hypohamiltonian graph
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 08/2018, Volume 88, Issue 4, pp. 551 - 557
We prove the titular statement. This settles a problem of Chvátal from 1973 and encompasses earlier results of Thomassen, who showed it for K3, and Collier and... 
05C10 | 05C45 | hypohamiltonian | induced subgraph | 05C60 | MATHEMATICS
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 10/2016, Volume 42, Issue 5, pp. 1247 - 1258
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2018, Volume 87, Issue 4, pp. 526 - 535
A graph G is hypohamiltonian/hypotraceable if it is not hamiltonian/traceable, but all vertex‐deleted subgraphs of G are hamiltonian/traceable. All known... 
hypotraceable graph | hamiltonian graph | hypohamiltonian graph | MATHEMATICS | PLANAR
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2017, Volume 340, Issue 8, pp. 1889 - 1896
Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we... 
Berge conjecture | Perfect matching cover | Hypohamiltonian graph | Cubic graph | Fulkerson conjecture | MATHEMATICS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2018, Volume 243, pp. 270 - 278
Consider a graph G in which the longest path has order |V(G)|−1. We denote the number of vertices v in G such that G−v is non-traceable with t . Gallai asked... 
Gallai's problem | Traceable | Hypotraceable | Almost hypotraceable | MATHEMATICS, APPLIED | NONEMPTY INTERSECTION | CYCLES | HYPOHAMILTONIAN GRAPHS | PLANAR | VERTICES | LONGEST PATHS | Computer science
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2018, Volume 88, Issue 1, pp. 40 - 45
A graph G is hypohamiltonian if G is non‐hamiltonian and for every vertex v in G, the graph G−v is hamiltonian. McKay asked in [J. Graph Theory 85 (2017) 7–11]... 
cubic | dot product | hamiltonian | planar | hypohamiltonian | MATHEMATICS | SNARKS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 443 - 459
The minimum leaf number ml(G) of a connected graph G is defined as the minimum number of leaves of the spanning trees of G if G is not hamiltonian and 1 if G... 
hamiltonian cycle | hypotraceable graph | hamiltonian path | hypohamiltonian graph | spanning tree | MATHEMATICS | PLANAR
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2017, Volume 85, Issue 1, pp. 7 - 11
A graph is called hypohamiltonian if it is not hamiltonian but becomes hamiltonian if any vertex is removed. Many hypohamiltonian planar cubic graphs have been... 
hypohamiltonian graph | planar graph | cubic graph | graph generation | MATHEMATICS | HYPOTRACEABLE GRAPHS
Journal Article
Opuscula Mathematica, ISSN 1232-9274, 2018, Volume 38, Issue 3, pp. 357 - 377
A graph \(G\) is called hypohamiltonian if \(G\) is not hamiltonian, but \(G-x\) is hamiltonian for each vertex \(x\) of \(G\). We present a list of 331... 
Forbidden configuration | Hypohamiltonian graph | Long cycle | forbidden configuration | long cycle | hypohamiltonian graph
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2011, Volume 67, Issue 1, pp. 55 - 68
We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu... 
hypohamiltonian | Hamiltonian | hypotraceable | graph | MATHEMATICS | HYPOTRACEABLE GRAPHS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2015, Volume 31, Issue 6, pp. 1821 - 1831
A digraph is hamiltonian if it has a cycle that visits every vertex. If a digraph $$D$$ D is nonhamiltonian and $$D-v$$ D - v is hamiltonian for every $$v\in... 
Mathematics | Engineering Design | Hypohamiltonian | Combinatorics | Oriented graphs | Digraphs | MATHEMATICS | Algebra
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 2018, Volume 25, Issue 4
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if... 
COLORINGS | MATHEMATICS | FULKERSON CONJECTURE | MATHEMATICS, APPLIED | CYCLE-DOUBLE COVERS | REDUCTION | PERFECT MATCHINGS | CONSTRUCTION | HYPOHAMILTONIAN SNARKS | RESISTANCE | EMBEDDINGS | ODDNESS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 02/2017, Volume 84, Issue 2, pp. 121 - 133
A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a Hamiltonian graph. Until now, the smallest known planar... 
hypotraceable graph | Grinberg's Theorem | hypohamiltonian graph | planar graph | graph generation | MATHEMATICS | HYPOTRACEABLE GRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 02/2019, Volume 90, Issue 2, pp. 189 - 207
Thomassen showed in 1978 that every planar hypohamiltonian graph contains a cubic vertex. Equivalently, a planar graph with minimum degree at least 4 in which... 
3‐connected | planar | hypohamiltonian | 3‐cut | 3-cut | 3-connected | MATHEMATICS | LONGEST PATHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 186, Issue 1, pp. 66 - 73
In this paper, a cycle is a graph in which each vertex has even degree. A Fulkerson-cover of a graph G is a set of six cycles such that each edge of G is in... 
Fulkerson-cover | 4-flow | Flip-flop | Hypohamiltonian | Fulkerson conjecture | MATHEMATICS, APPLIED | TUTTE | THEOREMS | FLOWS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2015, Volume 79, Issue 1, pp. 63 - 81
A graph G is almost hypohamiltonian if G is non‐hamiltonian, there exists a vertex w such that G−w is non‐hamiltonian, and for any vertex v≠w the graph G−v is... 
05C10 | Grinberg's Criterion | 05C45 | planar | hypohamiltonian | 05C38 | MATHEMATICS | HYPOTRACEABLE GRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 10/2017, Volume 86, Issue 2, pp. 223 - 243
We call a graph G a platypus if G is non‐hamiltonian, and for any vertex v in G, the graph G−v is traceable. Every hypohamiltonian and every hypotraceable... 
05C45 | non‐hamiltonian | hypohamiltonian | hypotraceable | traceable | 05C38 | non-hamiltonian | MATHEMATICS | LONGEST CYCLES | PLANAR
Journal Article
Ars Mathematica Contemporanea, ISSN 1855-3966, 2018, Volume 14, Issue 2, pp. 227 - 229
In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini's theorem from 1983 on hypohamiltonian snarks. However, their version... 
Snark | Irreducible snark | Hypohamiltonian | Dot product | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | snark | irreducible snark | COVERS | dot product | GRAPHS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2014, Volume 30, Issue 4, pp. 783 - 800
A digraph D of order n is r-hypohamiltonian (respectively r-hypotraceable) for some positive integer r < n − 1 if D is nonhamiltonian (nontraceable) and the... 
05C20 | hypohamiltonian | hypotraceable | Mathematics | Engineering Design | 2-hypohamiltonian | 2-hypotraceable | hypo-hypotraceable | Path Partition Conjecture | hypo-hypohamiltonian | Combinatorics | Traceability Conjecture | 05C38 | MATHEMATICS | DIGRAPHS | Graphs | Integers | Partitions | Construction | Deletion | Graph theory | Joints | Combinatorial analysis
Journal Article
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