On the general position problem on Kneser graphs

Patkós, Balázs

doi:10.26493/1855-3974.1957.a0f

Cited by 40 publications

(18 citation statements)

References 9 publications

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“…Following the seminal papers, the general position problem has been investigated in a sequence of papers [1,6,10,14,16,18,22,26]. As it happens, in the special case of hypercubes, the general position problem was studied back in 1995 by Körner [11] related to some coding theory problems.…”

Section: Introductionmentioning

confidence: 99%

On General Position Sets in Cartesian Products

et al. 2021

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The general position number $$\mathrm{gp}(G)$$ gp ( G ) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gp-sets of G. The general position number of cylinders $$P_r\,\square \,C_s$$ P r □ C s is deduced. It is proved that $$\mathrm{gp}(C_r\,\square \,C_s)\in \{6,7\}$$ gp ( C r □ C s ) ∈ { 6 , 7 } whenever $$r\ge s \ge 3$$ r ≥ s ≥ 3 , $$s\ne 4$$ s ≠ 4 , and $$r\ge 6$$ r ≥ 6 . A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in $$P_r\,\square \,P_s$$ P r □ P s , where $$r,s\ge 2$$ r , s ≥ 2 , is also determined.

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Section: Introductionmentioning

confidence: 99%

On General Position Sets in Cartesian Products

et al. 2021

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“…In [3], general position sets in graphs were characterized. Several additional papers on the concept followed, many of them dealing with bounds on the general position number and exact results in product graphs, Kneser graphs, and more, see [11,17,18,22,24,[26][27][28]. In addition, the concept was very recently extended to the Steiner general position number [16].…”

Section: Introductionmentioning

confidence: 99%

Zero forcing number versus general position number in tree-like graphs

Hua¹,

Hua²,

Klavžar³

2021

Preprint

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Let Z(G) and gp(G) be the zero forcing number and the general position number of a graph G, respectively. Known results imply that gp(T ) ≥ Z(T )+1 holds for every nontrivial tree T . It is proved that the result extends to block graphs. For connected, unicyclic graphs G it is proved that gp(G) ≥ Z(G). The result extends neither to bicyclic graphs nor to quasi-trees. Nevertheless, a large class of quasi-trees is found for which gp(G) ≥ Z(G) holds.

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“…But the same concept has already been studied two years earlier in [5] under the name geodetic irredundant sets. Refer [6,7,8,9,10,11] to understand the recent developments on general position number.…”

Section: Introductionmentioning

confidence: 99%

On independent position sets in graphs

Thomas¹,

Chandran²

2021

Proyecciones (Antofagasta)

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An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants.

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On the general position problem on Kneser graphs

Cited by 40 publications

References 9 publications

On General Position Sets in Cartesian Products

On General Position Sets in Cartesian Products

Zero forcing number versus general position number in tree-like graphs

On independent position sets in graphs

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