| 1. |
- Asratian, Armen, et al.
(författare)
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Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
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Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
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Tidskriftsartikel (refereegranskat)abstract
- An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
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| 2. |
- Kurujyibwami, Celestin
(författare)
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Admissible transformations and the group classification of Schrödinger equations
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
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| 3. |
- Casselgren, Carl Johan, et al.
(författare)
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Edge precoloring extension of hypercubes
- 2020
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Ingår i: Journal of Graph Theory. - : John Wiley & Sons. - 0364-9024 .- 1097-0118. ; 95:3, s. 410-444
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d − 1 edges of the d‐dimensional hypercube Qd can be extended to a proper d‐edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d‐edge colorings of Qd.
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| 4. |
- Eriksson, Kimmo, 1967-, et al.
(författare)
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The Chicken Braess Paradox
- 2019
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Ingår i: Mathematics Magazine. - : Taylor and Francis Inc.. - 0025-570X .- 1930-0980. ; 92:3, s. 213-221
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Tidskriftsartikel (refereegranskat)abstract
- Summary.: The Braess Paradox is the counterintuitive fact that creation of a shortcut may make travel slower. As each driver seeks to minimize his/her travel time, the shortcut may become so popular that it causes congestion elsewhere in the road network, thereby increasing the travel time for everyone. We extend the paradox by considering a shortcut that is a single-lane but two-way street. The conflict about which drivers get to use the single-lane shortcut is an example of a game theoretic situation known as Chicken, which merges with the Braess Paradox into the novel Chicken Braess Paradox: meeting traffic may make travel quicker.
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| 5. |
- Andren, Lina J., et al.
(författare)
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Avoiding Arrays of Odd Order by Latin Squares
- 2013
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Ingår i: Combinatorics, probability & computing. - : Cambridge University Press (CUP). - 0963-5483 .- 1469-2163. ; 22:2, s. 184-212
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Tidskriftsartikel (refereegranskat)abstract
- We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m andlt;= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -andgt; infinity.
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| 6. |
- Asratian, Armen, 1951-, et al.
(författare)
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Diskret matematik
- 2020. - 1
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Den här boken är främst avsedd för grundläggande kurser i diskret matematik vid universitet och högskolor. Framför allt riktar den sig till första- och andraårsstudenter på data-, matematik-, civilingenjörs- och högskoleingenjörsprogrammen.
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| 7. |
- Casselgren, Carl Johan, et al.
(författare)
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Completing partial Latin squares with one filled row, column and symbol
- 2013
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Ingår i: Discrete Mathematics. - : Elsevier. - 0012-365X .- 1872-681X. ; 313:9, s. 1011-1017
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Tidskriftsartikel (refereegranskat)abstract
- Let P be an n×n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbol s. Assume further that s is the symbol of cell (r,c) in P. We prove that P is completable to a Latin square if n≥8 and n is divisible by 4, or n≤7 and n∉{3,4,5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square.
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| 8. |
- Kamalian, Rafayel
(författare)
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On a number of colors in cyclically interval edgecolorings of trees
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A proper edge t-coloring of a graph G is a coloring of edges of G with colors 1,2,...,t such that each edge receives one color and no two adjacent edges receive the same color. A proper edge t-coloring of G is called a cyclically interval t-coloring if 1) at least one edge is colored k, for each k=1,2,...,t., and 2) for each vertex v of G the colors of edges incident with v are consecutive modulo t.We find, for an arbitrary tree G, all possible values of t for which G admits a cyclically interval t-coloring.
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| 9. |
- Thapper, Johan, 1977-
(författare)
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Combinatorial Considerations on Two Models from Statistical Mechanics
- 2007
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years.The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp.The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.
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| 10. |
- Izquierdo, Milagros, 1963-, et al.
(författare)
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Isometric Point-Circle Configurations on Surfaces from Uniform Maps
- 2016
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer-Verlag New York. - 2194-1009. ; 159, s. 201-212, s. 201-212
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Tidskriftsartikel (refereegranskat)abstract
- We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4'>v4v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.
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