### Abstract

A graph G on n vertices is called two-irregular if there are at most two vertices having the same degree for all possible degrees. We show that every graph with maximal degree at most n/8 - O(n ^{3/4}) can be embedded into a two-irregular graph. We obtain it as a corollary of an algorithmic proof of a result about packing the graphs. This improves the bound of O(n ^{1/4}) given by Faudree et al.

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

Pages (from-to) | 75-83 |

Number of pages | 9 |

Journal | Journal of Graph Theory |

Volume | 36 |

Issue number | 2 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Degree sequence
- Embedding
- Irregular
- Packing

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*36*(2), 75-83.

**Embedding of graphs in two-irregular graphs.** / Axenovich, M.; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 36, no. 2, pp. 75-83.

}

TY - JOUR

T1 - Embedding of graphs in two-irregular graphs

AU - Axenovich, M.

AU - Füredi, Z.

PY - 2001

Y1 - 2001

N2 - A graph G on n vertices is called two-irregular if there are at most two vertices having the same degree for all possible degrees. We show that every graph with maximal degree at most n/8 - O(n 3/4) can be embedded into a two-irregular graph. We obtain it as a corollary of an algorithmic proof of a result about packing the graphs. This improves the bound of O(n 1/4) given by Faudree et al.

AB - A graph G on n vertices is called two-irregular if there are at most two vertices having the same degree for all possible degrees. We show that every graph with maximal degree at most n/8 - O(n 3/4) can be embedded into a two-irregular graph. We obtain it as a corollary of an algorithmic proof of a result about packing the graphs. This improves the bound of O(n 1/4) given by Faudree et al.

KW - Degree sequence

KW - Embedding

KW - Irregular

KW - Packing

UR - http://www.scopus.com/inward/record.url?scp=25144487331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144487331&partnerID=8YFLogxK

M3 - Article

VL - 36

SP - 75

EP - 83

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -