### 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 language | English |
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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | Accepted/In press - Oct 30 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2015.12.012

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

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2015.12.012

}

TY - JOUR

T1 - Induced cycles in triangle graphs

AU - Lakshmanan S, Aparna

AU - Bujtás, Csilla

AU - Tuza, Zsolt

PY - 2014/10/30

Y1 - 2014/10/30

N2 - 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.

AB - 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.

KW - F-free graph

KW - Perfect graph

KW - Triangle graph

KW - Tuza's Conjecture

UR - http://www.scopus.com/inward/record.url?scp=84970031365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84970031365&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.12.012

DO - 10.1016/j.dam.2015.12.012

M3 - Article

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -