### Abstract

In section 1 some lower bounds are given for the maximal number of edges ofa (p - 1)- colorable partial graph. Among others we show that a graph on n vertices with m edges has a (p-1)-colorable partial graph with at least mT_{n.p}/(^{n}_{2}) edges, where T_{n.p} denotes the so called Turán number. These results are used to obtain upper bounds for special edge covering numbers of graphs. In Section 2 we prove the following theorem: If G is a simple graph and μ is the maximal cardinality of a triangle-free edge set of G, then the edges of G can be covered by μ triangles and edges. In Section 3 related questions are examined.

Original language | English |
---|---|

Pages (from-to) | 59-65 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 39 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1982 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*39*(1), 59-65. https://doi.org/10.1016/0012-365X(82)90040-1

**Triangle-free partial graphs and edge covering theorems.** / Lehel, J.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 39, no. 1, pp. 59-65. https://doi.org/10.1016/0012-365X(82)90040-1

}

TY - JOUR

T1 - Triangle-free partial graphs and edge covering theorems

AU - Lehel, J.

AU - Tuza, Z.

PY - 1982

Y1 - 1982

N2 - In section 1 some lower bounds are given for the maximal number of edges ofa (p - 1)- colorable partial graph. Among others we show that a graph on n vertices with m edges has a (p-1)-colorable partial graph with at least mTn.p/(n2) edges, where Tn.p denotes the so called Turán number. These results are used to obtain upper bounds for special edge covering numbers of graphs. In Section 2 we prove the following theorem: If G is a simple graph and μ is the maximal cardinality of a triangle-free edge set of G, then the edges of G can be covered by μ triangles and edges. In Section 3 related questions are examined.

AB - In section 1 some lower bounds are given for the maximal number of edges ofa (p - 1)- colorable partial graph. Among others we show that a graph on n vertices with m edges has a (p-1)-colorable partial graph with at least mTn.p/(n2) edges, where Tn.p denotes the so called Turán number. These results are used to obtain upper bounds for special edge covering numbers of graphs. In Section 2 we prove the following theorem: If G is a simple graph and μ is the maximal cardinality of a triangle-free edge set of G, then the edges of G can be covered by μ triangles and edges. In Section 3 related questions are examined.

UR - http://www.scopus.com/inward/record.url?scp=0040321493&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040321493&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(82)90040-1

DO - 10.1016/0012-365X(82)90040-1

M3 - Article

AN - SCOPUS:0040321493

VL - 39

SP - 59

EP - 65

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -