Induced cycles in triangle graphs

Aparna Lakshmanan S, Csilla Bujtás, Zsolt Tuza

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The triangle graph of a graph G, denoted by T(G), is the graph whose vertices represent the triangles (K3 subgraphs) of G, and two vertices of T(G) are adjacent if and only if the corresponding triangles share an edge. In this paper, we characterize graphs whose triangle graph is a cycle and then extend the result to obtain a characterization of Cn-free triangle graphs. As a consequence, we give a forbidden subgraph characterization of graph G for which T(G) is a tree, a chordal graph, or a perfect graph. For the class of graphs whose triangle graph is perfect, we verify a conjecture of the third author concerning packing and covering of triangles.

Original languageEnglish
JournalDiscrete Applied Mathematics
DOIs
Publication statusAccepted/In press - Oct 30 2014

Fingerprint

Triangle
Cycle
Graph in graph theory
Forbidden Subgraph
Triangle-free Graph
Perfect Graphs
Chordal Graphs
Packing
Subgraph
Covering
Adjacent
Verify
If and only if

Keywords

  • F-free graph
  • Perfect graph
  • Triangle graph
  • Tuza's Conjecture

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Induced cycles in triangle graphs. / Lakshmanan S, Aparna; Bujtás, Csilla; Tuza, Zsolt.

In: Discrete Applied Mathematics, 30.10.2014.

Research output: Contribution to journalArticle

Lakshmanan S, Aparna ; Bujtás, Csilla ; Tuza, Zsolt. / Induced cycles in triangle graphs. In: Discrete Applied Mathematics. 2014.
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