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On simplicial and co-simplicial vertices in graphs

✍ Scribed by Chı́nh T Hoàng; Stefan Hougardy; Frédéric Maffray; N.V.R Mahadev

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
286 KB
Volume
138
Category
Article
ISSN
0166-218X

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✦ Synopsis

We investigate the class of graphs deÿned by the property that every induced subgraph has a vertex which is either simplicial (its neighbours form a clique) or co-simplicial (its non-neighbours form an independent set). In particular we give the list of minimal forbidden subgraphs for the subclass of graphs whose vertex-set can be emptied out by ÿrst recursively eliminating simplicial vertices and then recursively eliminating co-simplicial vertices. ?

📜 SIMILAR VOLUMES

Well covered simplicial, chordal, and ci
Well covered simplicial, chordal, and circular arc graphs
✍ Prisner, Erich; Topp, Jerzy; Vestergaard, Preben Dahl 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 427 KB 👁 2 views

A graph G is called well covered if every two maximal independent sets of G have the same number of vertices. In this paper, we,characterize well covered simplicial, chordal and circular arc graphs.

A tight lower bound on the maximum genus
A tight lower bound on the maximum genus of a simplicial graph
✍ Jianer Chen; Saroja P. Kanchi; Jonathan L. Gross 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 856 KB

It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It