1. Extremal totally regular mixed graphs and partially oriented incidence graphs of projective and biaffine planesTatiana Bagin Jajcay, Robert Jajcay, György Kiss, István Porupsánszki, 2025, izvirni znanstveni članek Opis: An (r, z; g)-mixed graph is a graph containing both edges and darts satisfying the regularity property that each vertex of the graph is incident to r edges, z ingoing and z outgoing darts (called total regularity), and being of oriented girth g, i.e., containing an oriented cycle of length g, and no shorter oriented cycles. The problem addressed in this paper is analogous to the Cage Problem and calls for determining the orders of the smallest totally regular (r, z; g)-mixed graphs. We derive several upper and lower bounds on the orders of such minimal graphs, study the relations between these extremal graphs and their non-oriented or digraphical counterparts, and focus on properties of totally regular mixed graphs obtained by replacing some of the edges of the incidence graphs of projective and biaffine planes by darts. We also introduce two constructions based on introducing additional edges or darts into induced subgraphs of these incidence graphs.
Ključne besede: totally regular mixed graph, girth, projective plane, biaffine plane
Objavljeno v RUP: 04.06.2026; Ogledov: 54; Prenosov: 2
 Celotno besedilo (480,02 KB)
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2. Partial geometries with regular automorphism groups : master’s thesisAdisa Hodžić, 2024, magistrsko delo Ključne besede: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group
Objavljeno v RUP: 25.12.2024; Ogledov: 2348; Prenosov: 54
Celotno besedilo (1,22 MB) |
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4. Combinatorial configurations, quasiline arrangements, and systems of curves on surfacesJürgen Bokowski, Jurij Kovič, Tomaž Pisanski, Arjana Žitnik, 2018, izvirni znanstveni članek Ključne besede: pseudoline arrangement, quasiline arrangement, projective plane, incidence structure, combinatorial configuration, topological configuration, geometric configuration, sweep, wiring diagram, allowable sequence of permutations, maps on surfaces
Objavljeno v RUP: 03.01.2022; Ogledov: 2449; Prenosov: 32
Celotno besedilo (3,66 MB) |
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