# Václav Chvátal

V×¡clav Chv×¡tal | |
---|---|

V×¡clav Chv×¡tal (2007) | |

Born | Prague | 20 July 1946

Nationality | Canadian, Czech |

Fields | Mathematics, Computer Science, Operations Research |

Institutions | Concordia University |

Alma mater | University of Waterloo Charles University |

Doctoral advisor | Crispin Nash-Williams |

Doctoral students | David Avis (Stanford 1977) Bruce Reed (McGill 1986) |

Notable awards | Beale-Orchard-Hays Prize (2000) Docteur Honoris Causa, Universite de la Mediterranne (2003) Frederick W. Lanchester Prize (2007) John von Neumann Theory Prize (2015) |

### Biography

Václav (Vašek) Chvátal (Czech: [ˈvaːtslaf ˈxvaːtal] is a Teacher Emeritus in the Section of Computer Research and Software Anatomist at Concordia School in Montreal, Canada. He provides published thoroughly on topics in graph theory, combinatorics, and combinatorial marketing.

Chvátal was created in Prague in 1946 and informed in mathematics in Charles University or college in Prague, where he analyzed under the guidance of Zdeněk Hedrlín. He fled Czechoslovakia in 1968, three times following the Soviet invasion, and finished his Ph.D. in Mathematics in the University or college of Waterloo, beneath the guidance of Crispin St. J. A. Nash-Williams, in nov 1970. Subsequently, he required positions at McGill University or college (1971 and 1978-1986), Stanford University or college (1972 and 1974-1977), the Université de Montréal (1972-1974 and 1977-1978), and Rutgers University or college (1986-2004) before time for Montreal for the Canada Study Seat in Combinatorial Marketing at Concordia (2004-2011) as well as the Canada Research Seat in Discrete Mathematics (2011-2014) till his pension.

### Research

Chvátal first discovered of graph theory in 1964, in finding a reserve by Claude Berge within a Pilsen bookstore and far of his analysis involves graph theory: His initial mathematical publication, at age 19, concerned aimed graphs that can't be mapped to themselves by any non-trivial graph homomorphism Another graph-theoretic consequence of Chvátal was the 1970 structure of the tiniest feasible triangle-free graph that's both 4-chromatic and 4-regular, today referred to as the Chvátal graph. A 1972 paper relating Hamiltonian cycles to connection and maximum indie set size of the graph, gained Chvátal his Erdős amount of just one 1. Particularly, if there is an s in a way that confirmed graph is certainly s-vertex-connected and does not have any (s + 1)-vertex indie established, the graph should be Hamiltonian. Avis et al. inform the storyplot of Chvátal and Erdős training this result during the period of a long street trip, and afterwards thanking Louise Man "on her behalf steady generating." Within a 1973 paper, Chvátal presented the idea of graph toughness, a way of measuring graph connection that is carefully linked to the lifetime of Hamiltonian cycles. A graph is certainly t-tough if, for each k higher than 1, removing less than tk vertices leaves less than k linked components in the rest of the subgraph. For example, within a graph having a Hamiltonian routine, removing any nonempty group of vertices partitions the routine into for the most part as many items as the amount of eliminated vertices, therefore Hamiltonian graphs are 1-difficult. Chvátal conjectured that 3/2-difficult graphs, and later on that 2-difficult graphs, are usually Hamiltonian; despite later on researchers getting counterexamples to these conjectures, it still continues to be open up whether some continuous bound within the graph toughness will do to ensure Hamiltonicity.A few of Chvátal's function concerns groups of units, or equivalently hypergraphs, a topic already occurring in his Ph.D. thesis, where he also analyzed Ramsey theory. Inside a 1972 conjecture that Erdős known as "amazing" and "gorgeous", which remains open up (having a $10 reward provided by Chvátal because of its answer) he recommended that, in virtually any family of units closed beneath the procedure of acquiring subsets, the biggest pairwise-intersecting subfamily may continually be discovered by choosing some among the units and keeping all units containing that component. In 1979, he analyzed a weighted edition of the arranged cover issue, and proved a greedy algorithm provides great approximations to the perfect answer, generalizing earlier unweighted outcomes by David S. Johnson (J. Comp. Sys. Sci. 1974) and László Lovász (Discrete Mathematics. 1975).Chvátal 1st became thinking about linear development through the impact of Jack port Edmonds even though Chvátal was students in Waterloo. He quickly acknowledged the need for trimming planes for attacking combinatorial marketing problems such as for example computing maximum indie sets and, specifically, introduced the idea of a cutting-plane evidence. At Stanford in the 1970s, he started writing his well-known textbook, Linear Development, which was released in 1983.Cutting planes rest in the centre from the branch and cut technique used by effective solvers for the vacationing salesman issue. Between 1988 and 2005, the group of David L. Applegate, Robert E. Bixby, Vašek Chvátal, and William J. Make developed one particular solver, Concorde. The group was awarded The Beale-Orchard-Hays Award for Brilliance in Computational Mathematical Coding in 2000 because of their ten-page paper enumerating a few of Concorde's refinements from the branch and cut technique that resulted in the solution of the 13,509-town instance and it had been awarded the Frederick W. Lanchester Award in 2007 because of their book, The Vacationing Salesman Issue: A Computational Research.Chvátal can be known for proving the memorial theorem, for researching a self-describing digital series, for his use David Sankoff in the Chvátal–Sankoff constants controlling the behavior from the longest common subsequence issue on random inputs, as well as for his use Endre Szemerédi on hard situations for quality theorem proving.

### Books

Vašek Chvátal (1983). Linear Development. W.H. Freeman. ISBN 978-0-7167-1587-0. . Japanese translation released by Keigaku Shuppan, Tokyo, 1986. C. Berge and V. Chvátal (eds.) (1984). Topics on Ideal Graphs. Elsevier. ISBN 978-0-444-86587-8. CS1 maint: Extra text message: authors list (link) David L. Applegate; Robert E. Bixby; Vašek Chvátal; William J. Make (2007). The Journeying Salesman Issue: A Computational Research. Princeton College or university Press. ISBN 978-0-691-12993-8. CS1 maint: Multiple brands: authors list (link) Vašek Chvátal (ed.) (2011). Combinatorial Marketing: Strategies and Applications. IOS Press. ISBN 978-1-60750-717-8. CS1 maint: Extra text message: authors list (link)