2013/06/21 by David A. Cox, Cox, David A., Andrew Erskine +1 · 1 citation
Computer Science · Mathematics · #05C25 #05C75 (primary) #05C78 #13P10 (secondary) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph Labeling and Dimension Problems #Rings, Modules, and Algebras #math.AC #math.CO #msc:05C25 #msc:05C75 #msc:05C78 #msc:13P10
paper · pdf · doi:10.48550/arxiv.1306.5149
The paper "On Closed Graphs" (1306.5149v1) has been divided into two papers, "On Closed Graphs I", which is this arXiv submission, and "On Closed Graphs II", which will be a separate arXiv submission
openalex publication_date 2013/06/21 · arxiv created 2014/12/31 · arxiv updated 2015/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we prove that a connected graph has a closed labeling if and only if it is chordal, claw-free, and has a property we call narrow, which holds when every vertex is distance at most one from all longest shortest paths of the graph.