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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Satoshi Tagusari
Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan
Electrical & Electronics Engineering

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On strict-double-bound numbers of graphs and cut sets Kazutaka Ikeda; Kenjiro Ogawa; Satoshi Tagusari; Shin-ichiro Tashiro; Morimasa Tsuchiya
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.16

Abstract

For a poset P=(X,≤P), the strict-double-bound graph of P is the graph sDB(P) on V(sDB(P))=X for which vertices u and v of sDB(P) are adjacent if and only if u ≠ v and there exist elements x,y ∈ X distinct from u and v such that x ≤P u ≤P y and x ≤P v ≤P y. The strict-double-bound number ζ(G) of a graph G is defined as min{ n ; sDB(P) ≅ G ∪ Ǩn {for  some poset P}. We obtain an upper bound of strict-double-bound numbers of graphs with a cut-set generating a complete subgraph. We also estimate upper bounds of strict-double-bound numbers of chordal graphs.
Co-Authors Kazutaka Ikeda Kenjiro Ogawa Morimasa Tsuchiya Shin-ichiro Tashiro