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2. On the uniform structure of bipartite graphs admitting a dual adjacency matrix candidateBlas Fernández, Roghayeh Maleki, Štefko Miklavič, Giusy Monzillo, 2026, izvirni znanstveni članek Opis: Let Γ denote a finite, bipartite, connected graph with vertex set X. Fix x ∈ X and let ε ≥ 3 denote the eccentricity of x. For mutually distinct scalars {θ ∗ i }ε i=0 define a diagonal matrix A∗ = A∗(θ ∗ 0 , θ ∗ 1 , . . . , θ ∗ ε ) ∈ Mat X (R) as follows: for y ∈ X set (A∗)yy = θ ∗ ∂(x,y), where ∂ denotes the shortest path-length distance function of Γ. We say that A∗ is a dual adjacency matrix candidate of Γ with respect to x if the adjacency matrix A ∈ Mat X (R) of Γ and A∗ satisfy A3 A∗ − A∗ A3 + (β + 1)(A A∗ A2 − A2 A∗ A) = ρ(A A∗ − A∗ A) for some scalars β, ρ ∈ R. In this paper, we investigate when bipartite graphs that admit a dual adjacency matrix candidate also admit a uniform structure (in the sense of Terwilliger [6]). To do that, we first define a weakly uniform structure by slightly relaxing the conditions of uniform structure. The main result of this paper is that Γ admits a dual adjacency matrix candidate with respect to x if and only if Γ admits a weakly uniform structure with respect to x whose parameters satisfy some additional conditions. In particular, for β = 2, the weakly uniform structure is indeed a uniform structure.
Ključne besede: uniform property, dual adjacency matrix, Q-polynomial property
Objavljeno v RUP: 18.06.2026; Ogledov: 490; Prenosov: 10
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3. Conformal hypergraphs : duality and implications for the upper clique transversal problemEndre Boros, Vladimir Gurvich, Martin Milanič, Yushi Uno, 2025, izvirni znanstveni članek Opis: Given a hypergraph H, the dual hypergraph of H is the hypergraph of all minimal transversals of H. The dual hypergraph is always Sperner, that is, no hyperedge contains another. A special case of Sperner hypergraphs are the conformal Sperner hypergraphs, which correspond to the families of maximal cliques of graphs. All these notions play an important role in many fields of mathematics and computer science, including combinatorics, algebra, database theory, etc. In this paper we study conformality of dual hypergraphs and prove several results related to the problem of recognizing this property. In particular, we show that the problem is in co-NP and can be solved in polynomial time for hypergraphs of bounded dimension. In the special case of dimension 3, we reduce the problem to 2-Satisfiability. Our approach has an implication in algorithmic graph theory: we obtain a polynomial-time algorithm for recognizing graphs in which all minimal transversals of maximal cliques have size at most k, for any fixed k.
Ključne besede: conformal hypergraph, dual hypergraph, hypergraph, maximal clique, upper clique transversal
Objavljeno v RUP: 25.09.2025; Ogledov: 1644; Prenosov: 12
Celotno besedilo (475,86 KB)
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4. The distance function on Coxeter-like graphs and self-dual codesMarko Orel, Draženka Višnjić, 2025, izvirni znanstveni članek Ključne besede: Coxeter graph, invertible symmetric matrices, binary field, rank, distance in graphs, alternate matrices, self-dual codes
Objavljeno v RUP: 30.05.2025; Ogledov: 1500; Prenosov: 24
Celotno besedilo (1,26 MB)
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7. Načrti in Hadamardove matrike : zaključna nalogaMateja Grižon, 2020, diplomsko delo Ključne besede: t-načrt, končna projektivna ravnina, Steinerjev sistem, incidenčna matrika, simetrični načrt, dual načrta, permutacijska grupa, avtomorzem načrta, skrčitev načrta, razširitev načrta, Hadamardova matrika, Hadamardov načrt
Objavljeno v RUP: 02.10.2020; Ogledov: 3240; Prenosov: 34
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8. Qiao, Zhi, Koolen, Jack: A new characterization of the dual polar graphs. (English summary). - J. Combin. Theory Ser. B 135 (2019), 200-211Safet Penjić, 2020, recenzija, prikaz knjige, kritika Ključne besede: Distance-regular graph, dual polar graph, Delsarte clique
Objavljeno v RUP: 15.04.2020; Ogledov: 4698; Prenosov: 19
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9. Sprague-Grundy function of matroids and related hypergraphsEndre Boros, Vladimir Gurvich, Nhan Bao Ho, Kazuhisa Makino, Peter Muršič, 2019, izvirni znanstveni članek Ključne besede: matroid, self-dual matroid, impartial game, Sprague-Grundy function, Nim, hypergraph Nim, JM hypergraph
Objavljeno v RUP: 11.02.2020; Ogledov: 3432; Prenosov: 106
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