Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sun, 26 Jan 2020 11:08:26 GMT2020-01-26T11:08:26Z10441Decomposing four-manifolds up to homotopy typehttp://hdl.handle.net/11380/309535Titolo: Decomposing four-manifolds up to homotopy type
Abstract: Let M be a closed connected oriented topological 4-manifold. Suppose that there is a degree one map f from M to another closed topological 4-manifold P, which induces an isomorphism between the fundamental groups. We give a homological condition on the integer intersection form of M and on the intersection form of M over the integral group ring of its fundamental group under which M is homotopy equivalent to a connected sum of P with a simply-connected closed topological 4-manifold M'. This gives a partial solution to a conjecture of Hillman stated in Bull. London Math. Soc. 27 (1995). Then some splitting results for closed 4-manifolds with special homotopy complete the paper.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/3095352003-01-01T00:00:00ZA survey on snarks and new results: Products, reducibility and a computer searchhttp://hdl.handle.net/11380/309541Titolo: A survey on snarks and new results: Products, reducibility and a computer search
Abstract: In this paper we survey recent results and problems of both theoretical and algorithmic character on the construction of snarks-non-trivial cubic graphs of class two, of cyclic edge-connectivity at least 4 and with girth greater than or equal to 5. We next study the process, also considered by Cameron, Chetwynd, Watkins, Isaacs, Nedela, and Skoviera, of splitting a snark into smaller snarks which compose it. This motivates an attempt to classify snarks by recognizing irreducible and prime snarks and proving that all snarks can be constructed from them. As a consequence of these splitting operations, it follows that any snark (other than the Petersen graph) of order less than or equal to 26 can be built as either a dot product or a square product of two smaller snarks. Using a new computer algorithm we have confirmed the computations of Brinkmann and Steffen on the classification of all snarks of order less than 30. Our results recover the well-known classification of snarks of order not exceeding 22. Finally, we prove that any snark G of order less than or equal to 26 is almost Hamiltonian, in the sense that G has at least one vertex v for which G\v is Hamiltonian.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/11380/3095411998-01-01T00:00:00ZOn spines of Seifert fibered manifoldshttp://hdl.handle.net/11380/310067Titolo: On spines of Seifert fibered manifolds
Abstract: We define a family of balanced presentations of groups and prove that they correspond to spines of some Seifert fibered 3-manifolds. These presentations of groups (and manifolds) generalize in a natural way many classes of presentations of groups (and manifolds) previously studied by several authors. Moreover, we construct crystallizations representing the small Seifert manifolds of the considered class.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/3100672003-01-01T00:00:00ZMatrici, Ranghi e Sistemi Linearihttp://hdl.handle.net/11380/1164136Titolo: Matrici, Ranghi e Sistemi Lineari
Abstract: Questo fascicolo fa parte di una serie di fascicoli (si veda bibliografia interna) di Matematica della Teoria di Algebra Lineare e tratta della Teoria delle Matrici, dei Ranghi e dei Sistemi Lineari. L’ultima parte trattata da codesto fascicolo presuppone l’acquisizione di alcune nozioni di Algebra Lineare, tutte già affrontate nei fascicoli precedentemente pubblicati. La novità di questo fascicolo rispetto agli altri risulta in una trattazione sistematica della Teoria delle Matrici, dei Ranghi e dei Sistemi Lineari il cui sviluppo nei Libri di Algebra Lineare si trova svolto in maniera frammentato in quanto presuppone lo svolgimento (tra un argomento e l’altro) di altri concetti: lineare indipendenza, dimensione di sottospazi vettoriali, determinanti etc.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11380/11641362018-01-01T00:00:00ZOn the automorphic chromatic index of a graphhttp://hdl.handle.net/11380/644808Titolo: On the automorphic chromatic index of a graph
Abstract: We define the automorphic H-chromatic index of a graph G as the minimum integer m for which G has a proper edge-coloring with m colors which is preserved by a given automorphism group H of G. After the description of some properties, we determine upper bounds for this index when H is a cyclic group of prime order. We also show that these upper bounds are best possible in a number of istances.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/6448082008-01-01T00:00:00ZTree-designs with balanced-type conditionshttp://hdl.handle.net/11380/704336Titolo: Tree-designs with balanced-type conditions
Abstract: For a given graph G we say that a G-design is balanced if there exists a constant r such that for each point x the number of blocks containing x is equal to r. A G-design is degree-balanced if, for each degree d occurring in the graph G, there exists a constant r_d such that, for each point x, the number of blocks containing x as a vertex of degree d is equal to r_d.Let V_1, V_2, . . . , V_h be the vertex-orbits of G under its automorphism group. A G-design is said to be orbit-balanced (or strongly balanced) if for i = 1, 2, . . . , h there exists a constant R_i such that, for each point x the number of blocks of the G-design in which x occurs as an element in the orbit V_i is equal to R_i.If G is a tree with six vertices, we determine the values of v for which a balanced G-design with v points exists, the values of v for which a degree-balanced G-design with v points exists, and the values of v for which an orbit-balanced G-design with v points exists.We also consider the existence problem for G-designs which are not balanced, which are balanced but not degree-balanced, and which are degree-balanced but not orbit-balanced.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11380/7043362013-01-01T00:00:00ZOn the computation of L-groups and natural mapshttp://hdl.handle.net/11380/310848Titolo: On the computation of L-groups and natural maps
Abstract: In this paper we compute surgery (resp. splitting) obstruction groups, here called L-groups, and natural maps for many diagrams of oriented finite (not necessary abelian) 2-groups and homomorphisms which preserve orientations.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/11380/3108482002-01-01T00:00:00ZSpecial classes of snarkshttp://hdl.handle.net/11380/310215Titolo: Special classes of snarks
Abstract: We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then we study many classes of snarks satisfying certain additional conditions, and investigate the relationships among them. Finally, we discuss connections between the snark family and some significant conjectures of graph theory, and list some problems and open questions which arise naturally in this research.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/3102152003-01-01T00:00:00ZSplittings of manifolds with boundary and related invariantshttp://hdl.handle.net/11380/451006Titolo: Splittings of manifolds with boundary and related invariants
Abstract: We construct special handle decompositions for a compact connected PL manifold with non empty boundary and study the associated topological invariants. As a consequence, we characterize the unknot in the (n+2)-sphere (n less or equal 2) as the unique n-knot whose complement has genus one. Then we obtain a simple geometric proof of the non cancellation theorem for tame n-knots in the (n+2)-sphere, for n less or equal 2.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11380/4510061993-01-01T00:00:00ZSymmetric bowtie decompositions of the complete graphhttp://hdl.handle.net/11380/644538Titolo: Symmetric bowtie decompositions of the complete graph
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6445382010-01-01T00:00:00Z