A note on 3-Steiner intervals and betweenness

Changat, Manoj; Lakshmikuttyamma, Anandavally K.; Mathews, J. Howard; Peterin, Iztok; Narasimha-Shenoi, Prasanth G.; Tepeh, Aleksandra

doi:10.1016/j.disc.2011.08.009

Cited by 10 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further results involving Steiner tree problems related to geodesic convexity in graphs can be found in [15,18,26,28,47,55,96,115,116,136,150,152,155,172,180].…”

Section: Theorem 512 ([119]) Every Edge Steiner Set Of a Connected mentioning

confidence: 99%

Geodesic Convexity in Graphs

Pelayo¹

2013

SpringerBriefs in Mathematics

View full text Add to dashboard Cite

SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied School of Agricultural Engineering of Barcelona

show abstract

“…Further results involving Steiner tree problems related to geodesic convexity in graphs can be found in [15,18,26,28,47,55,96,115,116,136,150,152,155,172,180].…”

Section: Theorem 512 ([119]) Every Edge Steiner Set Of a Connected mentioning

confidence: 99%

Geodesic Convexity in Graphs

Pelayo¹

2013

SpringerBriefs in Mathematics

View full text Add to dashboard Cite

show abstract

“…Since then many papers have appeared on the topic. For a small collection see [1,4,9,13,14,20,22,25,28] and the references therein. In particular, note that Steiner number was introduced by Chartrand and Zhang in [14].…”

Section: Introductionmentioning

confidence: 99%

“…In [4,9] the authors worked on a variation of the Steiner problem, namely for multi sets (instead of sets). These definitions coincide for Steiner convexity, since we take all subsets of C in the definition of a Steiner convex set C and not only k-subsets of C for a fixed k. (The latter is known as the k-Steiner convexity.)…”

Section: Introductionmentioning

confidence: 99%

Some Steiner concepts on lexicographic products of graphs

Anand

Changat

Peterin

et al. 2014

Discrete Math. Algorithm. Appl.

Self Cite

View full text Add to dashboard Cite

Let G be a graph and W a subset of V(G). A subtree with the minimum number of edges that contains all vertices of W is a Steiner tree for W. The number of edges of such a tree is the Steiner distance of W and union of all vertices belonging to Steiner trees for W form a Steiner interval. We describe both of these for the lexicographic product of graphs. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number.

show abstract

Introduction

Pelayo¹

2013

Geodesic Convexity in Graphs

View full text Add to dashboard Cite

A note on 3-Steiner intervals and betweenness

Cited by 10 publications

References 14 publications

Geodesic Convexity in Graphs

Geodesic Convexity in Graphs

Some Steiner concepts on lexicographic products of graphs

Introduction

Contact Info

Product

Resources

About