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Generalization of edge general position problem
Paul Manuel, R. Prabha, Sandi Klavžar, 2025, izvirni znanstveni članek

Opis: The edge geodesic cover problem of a graph G is to find a smallest number of geodesics that cover the edge set of G. The edge k-general position problem is introduced as the problem to find a largest set S of edges of G such that at most k-1 edges of S lie on a common geodesic. We show that these are dual min-max problems and connect them to an edge geodesic partition problem. Using these connections, exact values of the edge k-general position number is determined for different values of k and for various networks including torus networks, hypercubes, and Benes networks.
Ključne besede: general position set, edge geodesic cover problem, edge k-general position problem, torus network, hypercube, Benes network
Objavljeno v RUP: 03.11.2025; Ogledov: 155; Prenosov: 1
Celotno besedilo (812,56 KB)

On some extremal position problems for graphs
James Tuite, Elias John Thomas, Ullas Chandran S.V., 2025, izvirni znanstveni članek

Opis: The general position number of a graph G is the size of the largest set of vertices S such that no geodesic of G contains more than two elements of S. The monophonic position number of a graph is defined similarly, but with `induced path' in place of `geodesic'. In this paper we investigate some extremal problems for these parameters. Firstly we discuss the problem of the smallest possible order of a graph with given general and monophonic position numbers. We then determine the asymptotic order of the largest size of a graph with given general or monophonic position number, classifying the extremal graphs with monophonic position number two. Finally we establish the possible diameters of graphs with given order and monophonic position number.
Ključne besede: general position, monophonic position, Turán problems, size, diameter, induced path
Objavljeno v RUP: 21.10.2025; Ogledov: 207; Prenosov: 0
Celotno besedilo (396,13 KB)

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