1. Induced minor models : Structural properties and algorithmic consequencesNicolas Bousquet, Clément Jean Dallard, Maël Dumas, Claire Hilaire, Martin Milanič, Anthony Perez, Nicolas Trotignon, 2026, izvirni znanstveni članek Opis: A graph H is an induced minor of G if there exists an induced minor model of H in G, that is, a collection of pairwise disjoint subsets of vertices of G labeled by the vertices of H, each inducing a connected subgraph in G, such that two vertices of H are adjacent if and only if there is an edge in G between the corresponding subsets. In this paper, we investigate structural properties of induced minor models, including bounds on treewidth and chromatic number of the subgraphs induced by minimal induced minor models. As algorithmic applications of our structural results, we make use of recent developments regarding tree-independence number to show that if H is the 4-wheel, the 5-vertex complete graph minus an edge, or a complete bipartite graph K2,q , then there is a polynomial-time algorithm to find in a given graph G an induced minor model of H in G, if there is one. We also develop an alternative polynomial-time algorithm for recognizing graphs that do not contain K2,3 as an induced minor, which revolves around the idea of detecting the induced subgraphs whose presence is forced when the input graph contains K2,3 as an induced minor. It turns out that all these induced subgraphs are Truemper configurations.
Ključne besede: induced minor, treewidth, chromatic number, tree-independence number, Truemper configuration
Objavljeno v RUP: 16.12.2025; Ogledov: 287; Prenosov: 3
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2. On (r,g,χ)- graphs and cages of regularity r, girth g and chromatic number χGabriela Araujo-Pardo, Julio César Díaz-Calderón, Julián Fresán-Figueroa, Diego González-Moreno, Linda Lesniak, Mika Olsen, 2025, izvirni znanstveni članek Opis: For integers r ≥ 2, g ≥ 3 and χ ≥ 2, an (r, g, χ)-graph is an r-regular graph with girth g and chromatic number χ. Such a graph of minimum order is called an (r, g, χ)-cage. Here we prove the existence of (r, g, χ)-graphs for all r and even g when χ = 2 and for all r and g when χ = 3. Furthermore, using both existence proofs and explicit constructions we give examples of (r, g, χ)-graphs for infinitely many values of r, g, χ.
Ključne besede: graphs, cages, girth, chromatic number
Objavljeno v RUP: 03.11.2025; Ogledov: 389; Prenosov: 3
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3. Banff designs: difference methods for coloring incidence graphsMarco Buratti, Francesca Merola, Anamari Nakić, Christian Rubio-Montiel, 2025, izvirni znanstveni članek Opis: We present some results on the harmonious colourings of the Levi graph of a 2-design, focusing on Steiner 2-design. It is easily seen that the harmonious chromatic number of such a Levi graph is at least the number of points of the design: we study and construct Banff designs, that is designs such that this lower bound is attained.
Ključne besede: Harmonious chromatic number, Levi graph, combinatorial design
Objavljeno v RUP: 03.11.2025; Ogledov: 363; Prenosov: 6
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4. On the balanced upper chromatic number of finite projective planesZoltán L. Blázsik, Aart Blokhuis, Štefko Miklavič, Zoltán Lóránt Nagy, Tamás Szőnyi, 2021, izvirni znanstveni članek Ključne besede: projective planes, balanced upper chromatic number, difference sets, planar functions, probabilistic method
Objavljeno v RUP: 18.01.2021; Ogledov: 2649; Prenosov: 40
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