n-ary transit functions in graphs

Changat, Manoj; Mathews, J. Howard; Narasimha-Shenoi, Prasanth G.; Peterin, Iztok

doi:10.7151/dmgt.1522

Cited by 8 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Transit function or 2-ary functions have been generalized to k arguments to generalize convexities generated by k-ary functions [14]. For n-ary convexities, also refer [28].…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…Condition (kKR) was introduced in [14]. A necessary condition for R to explain X is that every set C ∈ X is identified by at most k distinct points.…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…First we note that (kt3) and (KS) ensure that X and the collection of transit sets both contain all singletons. As shown in [14], (kKR) is equivalent to X ⊆ {R(u 1 , . .…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…For a given set system X , the minimal value of k for which (kKR) holds is called the arity of X [14].…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…The arity of a convexity [14] is the smallest integer (which exists since V is finite in our setting) such that…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

See 4 more Smart Citations

Axiomatic characterization of transit functions of weak hierarchies

Changat

Narasimha-Shenoi²,

Stadler

2018

Art Discrete Appl. Math.

Self Cite

View full text Add to dashboard Cite

Transit functions provide a unified approach to study notions of intervals, convexities, and betweenness. Recently, their scope has been extended to certain set systems associated with clustering. We characterize here the class of set systems that correspond to k-ary monotonic transit functions. Convexities form a subclass and are characterized in terms of transit functions by two additional axioms. We then focus on axiom systems associated with weak hierarchies as well as other generalizations of hierarchical set systems. c b This work is licensed under http://creativecommons.org/licenses/by/3.0/ 2 Set systems identified by transit functions Throughout this contribution, V is a finite, non-empty set. Consider an arbitrary set system X ⊆ 2 V and the function R X (x, y) ={A ∈ X | x, y ∈ A}.(2.1)

show abstract

“…Transit function or 2-ary functions have been generalized to k arguments to generalize convexities generated by k-ary functions [14]. For n-ary convexities, also refer [28].…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…Condition (kKR) was introduced in [14]. A necessary condition for R to explain X is that every set C ∈ X is identified by at most k distinct points.…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…First we note that (kt3) and (KS) ensure that X and the collection of transit sets both contain all singletons. As shown in [14], (kKR) is equivalent to X ⊆ {R(u 1 , . .…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…For a given set system X , the minimal value of k for which (kKR) holds is called the arity of X [14].…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

“…The arity of a convexity [14] is the smallest integer (which exists since V is finite in our setting) such that…”

Section: Transit Functions With Arity >mentioning

confidence: 99%

See 3 more Smart Citations