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Sabidussi, Gert

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Retired professor

Faculty of Arts and Science - Department of Mathematics and Statistics

André-Aisenstadt

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Student supervision Expand all Collapse all

Droites sur les hypergraphes Theses and supervised dissertations / 2014-07
Bayani, Aryan
Abstract
The Sylvester-Gallai theorem states that in a finite set S of points in the plane, not all on the same line, there is a line passing through exactly two points of S. Chvátal [14] extended the concept of lines to arbitrary metric spaces and made a conjecture generalizing the Sylvester-Gallai theorem. Chen [10] proved this conjecture which is now called The Sylvester-Chvátal Theorem. In 1943, Erdos [18] noticed a corollary to the Sylvester-Gallai theorem stating that, in a finite set V of points in the plane, not all on a line, the number of lines that pass through at least two points of V is at least |V |. De Bruijn et Erdos [7] generalized this corollary, using a generalized definition of a line (see Chapter 2) and proved that any set of n points, not all on the same line, determines at least n distinct lines. In this master’s thesis, we will study the theorems mentioned above. We will also look at the Theorem of De Bruijn-Erdos within the framework of hypergraphs and various metric spaces.

Link to the Papyrus's document

Dimension métrique des graphes Theses and supervised dissertations / 2008
Bernard, Samuel
Abstract
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Link to the Papyrus's document

Les graphes asymétriques minimaux de longueur induite 3 Theses and supervised dissertations / 2006
Gagnon, Jérôme
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Automorphismes et isomorphismes des graphes de Cayley Theses and supervised dissertations / 2004
Fournier, J.
Abstract
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Selected publications Expand all Collapse all

Automorphism group and diameter of a graph

Dankelmann, P., Erwin, D., Mukwembi, S., Rodrigues, B. G., Mwambene, E. et Sabidussi, G., Automorphism group and diameter of a graph 70, 80--91 (2012), , J. Graph Theory

Maximum independent sets in 3- and 4-regular Hamiltonian graphs

Fleischner, Herbert, Sabidussi, Gert et Sarvanov, Vladimir I., Maximum independent sets in 3- and 4-regular Hamiltonian graphs 310, 2742--2749 (2010), , Discrete Math.

On the geodesic pre-hull number of a graph

Polat, Norbert et Sabidussi, Gert, On the geodesic pre-hull number of a graph 30, 1205--1220 (2009), , European J. Combin.

Embedding graphs as isometric medians

Dankelmann, P. et Sabidussi, G., Embedding graphs as isometric medians 156, 2420--2422 (2008), , Discrete Appl. Math.

Deeply asymmetric planar graphs

Aksionov, V. A., Borodin, O. V., Melnikov, L. S., Sabidussi, G., Stiebitz, M. et Toft, B., Deeply asymmetric planar graphs 95, 68--78 (2005), , J. Combin. Theory Ser. B

3-colorability of 4-regular Hamiltonian graphs

Fleischner, Herbert et Sabidussi, Gert, 3-colorability of 4-regular Hamiltonian graphs 42, 125--140 (2003), , J. Graph Theory

Parity equivalence in Eulerian graphs

Sabidussi, Gert, Parity equivalence in Eulerian graphs 24, 249--256 (1997), , J. Graph Theory

Decomposing the countable complete graph into isomorphic spanning subgraphs

King, Andrew J. H., Dufour, Matthieu et Sabidussi, Gert, Decomposing the countable complete graph into isomorphic spanning subgraphs 113, 81--100 (1996), , Congr. Numer.

Graphs without dead ends

Sabidussi, Gert, Graphs without dead ends 17, 69--87 (1996), , European J. Combin.

Modular Nim

Fraenkel, Aviezri S., Jaffray, Alan, Kotzig, Anton et Sabidussi, Gert, Modular Nim 143, 319--333 (1995), , Theoret. Comput. Sci.

Factorisation of $4$-regular graphs and Petersen's theorem

Kouider, Mekkia et Sabidussi, Gert, Factorisation of $4$-regular graphs and Petersen's theorem 63, 170--184 (1995), , J. Combin. Theory Ser. B

Fixed elements of infinite trees

Polat, Norbert et Sabidussi, Gert, Fixed elements of infinite trees 130, 97--102 (1994), , Discrete Math.

Binary invariants and orientations of graphs

Sabidussi, Gert, Binary invariants and orientations of graphs 101, 251--277 (1992), , Discrete Math.

Edge orbits and edge-deleted subgraphs

Andersen, Lars Døvling, Ding, Song Kang, Sabidussi, Gert et Vestergaard, Preben Dahl, Edge orbits and edge-deleted subgraphs 8, 31--44 (1992), , Graphs Combin.

Julius Petersen 1839--1910. A biography

Lützen, Jesper, Sabidussi, Gert et Toft, Bjarne, Julius Petersen 1839--1910. A biography 100, 5--82 (1992), , Discrete Math.

Julius Petersen annotated bibliography

Christiansen, Margit, Lützen, Jesper, Sabidussi, Gert et Toft, Bjarne, Julius Petersen annotated bibliography 100, 83--97 (1992), , Discrete Math.

Correspondence between Sylvester, Petersen, Hilbert and Klein on invariants and the factorisation of graphs 1889--1891

Sabidussi, Gert, Correspondence between Sylvester, Petersen, Hilbert and Klein on invariants and the factorisation of graphs 1889--1891 100, 99--155 (1992), , Discrete Math.

Transforming Eulerian trails

Fleischner, H., Sabidussi, G. et Wenger, E., Transforming Eulerian trails 109, 103--116 (1992), , Discrete Math.

Minimal asymmetric graphs of induced length $4$

Ne\v set\v ril, Jaroslav et Sabidussi, Gert, Minimal asymmetric graphs of induced length $4$ 8, 343--359 (1992), , Graphs Combin.

Anton Kotzig (1919--1991)

Abrham, Jaromír, Rosa, Alexander, Sabidussi, Gert et Turgeon, Jean M., Anton Kotzig (1919--1991) 3, 100--104 (1991), , Bull. Inst. Combin. Appl.

Asymmetrising sets in trees

Polat, Norbert et Sabidussi, Gert, Asymmetrising sets in trees 95, 271--289 (1991), , Discrete Math.

Clumps, minimal asymmetric graphs, and involutions

Sabidussi, Gert, Clumps, minimal asymmetric graphs, and involutions 53, 40--79 (1991), , J. Combin. Theory Ser. B

Focality and graph isomorphism

Imrich, W. et Sabidussi, G., Focality and graph isomorphism 81, 237--245 (1990), , Discrete Math.

Gleichungen für nichtassoziative Graphenprodukte

Sabidussi, Gert, Gleichungen für nichtassoziative Graphenprodukte 198, 249--265 (1989), , Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II

Paths in bipartite graphs with color-inverting involutions

Sabidussi, Gert, Paths in bipartite graphs with color-inverting involutions 13, 157--174 (1989), , J. Graph Theory

Graphs with antipodal properties and given automorphism group

Sabidussi, Gert, Graphs with antipodal properties and given automorphism group 1, 101--109 (1988), , Sci. Ser. A Math. Sci. (N.S.)

Color-reversal by local complementation

Sabidussi, Gert, Color-reversal by local complementation 64, 81--86 (1987), , Discrete Math.

On maps related to Halin separation lattices

Sabidussi, Gert, On maps related to Halin separation lattices 6, 257--264 (1985), , European J. Combin.

Recursive undecidability of the binding property for finitely presented equational classes

Földes, Stéphane et Sabidussi, Gert, Recursive undecidability of the binding property for finitely presented equational classes 12, 1--4 (1981), , Algebra Universalis

Une généralization du théorème de Ginsburg-Rose

Chaput, Daniel et Sabidussi, Gert, Une généralization du théorème de Ginsburg-Rose 32, 567--575 (1980), , Canad. J. Math.

On semigroups of graph endomorphisms

Földes, S. et Sabidussi, G., On semigroups of graph endomorphisms 30, 117--120 (1980), , Discrete Math.

Hamiltonian cubic graphs and centralizers of involutions

Babai, László, Frankl, Peter, Kollár, János et Sabidussi, Gert, Hamiltonian cubic graphs and centralizers of involutions 31, 458--464 (1979), , Canad. J. Math.

Uniforme Ráume in der Graphentheorie

Sabidussi, Gert, Uniforme Ráume in der Graphentheorie , Ber. No. 104, 5 (1978), , Ber. Math.-Statist. Sekt. Forsch. Graz

Weak separation lattices of graphs

Sabidussi, Gert, Weak separation lattices of graphs 28, 691--724 (1976), , Canad. J. Math.

Meshes on $3$-connected graphs

Sabidussi, Gert, Meshes on $3$-connected graphs 1, 269--276 (1971), , Discrete Math.

Idempotency of circuit-induced exchange operators

Sabidussi, Gert, Idempotency of circuit-induced exchange operators 74, 330--335 (1970), , Monatsh. Math.

Existence and structure of self-adjoint graphs

Sabidussi, Gert, Existence and structure of self-adjoint graphs 104, 257--280 (1968), , Math. Z.

Sequences of Euler graphs

Sabidussi, Gert, Sequences of Euler graphs 9, 177--182 (1966), , Canad. Math. Bull.

The centrality index of a graph

Sabidussi, Gert, The centrality index of a graph 31, 581--603 (1966), , Psychometrika

Vertex-transitive graphs

Sabidussi, Gert, Vertex-transitive graphs 68, 426--438 (1964), , Monatsh. Math.

Infinite Euler graphs

Sabidussi, Gert, Infinite Euler graphs 16, 821--838 (1964), , Canad. J. Math.

Minimal isthmoids

Sabidussi, Gert, Minimal isthmoids 66, 346--350 (1962), , Monatsh. Math.

The lexicographic product of graphs

Sabidussi, Gert, The lexicographic product of graphs 28, 573--578 (1961), , Duke Math. J.

Graph derivatives

Sabidussi, Gert, Graph derivatives 76, 385--401 (1961), , Math. Z.

Graphs with given infinite group

Sabidussi, Gert, Graphs with given infinite group 64, 64--67 (1960), , Monatsh. Math.

Graph multiplication

Sabidussi, Gert, Graph multiplication 72, 446--457 (1959), , Math. Z.

The composition of graphs

Sabidussi, Gert, The composition of graphs 26, 693--696 (1959), , Duke Math. J

On the minimum order of graphs with given automorphism group

Sabidussi, Gert, On the minimum order of graphs with given automorphism group 63, 124--127 (1959), , Monatsh. Math.

On a class of fixed-point-free graphs

Sabidussi, Gert, On a class of fixed-point-free graphs 9, 800--804 (1958), , Proc. Amer. Math. Soc.

Graphs with given group and given graph-theoretical properties

Sabidussi, Gert, Graphs with given group and given graph-theoretical properties 9, 515--525 (1957), , Canad. J. Math.

Loewy-groupoids related to linear graphs

Sabidussi, Gert, Loewy-groupoids related to linear graphs 76, 477--487 (1954), , Amer. J. Math.