### Abstract

If the monochromatic graphs G^{1} and G^{2} in a 2-edge-coloured complete graph K_{m} (m ≥ 6) are connected, then there exist at least two vertices x such that the graphs G^{1}\x and G^{2}\x are also connected. Similar theorems are proved for k-edge-coloured complete graphs. They generalize earlier results of Idzik et al. [Discrete Math. 66 (1987) 119-125]. Examples are shown that analogous theorems are no longer true for 3-uniform complete hypergraphs.

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

Pages (from-to) | 301-306 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 235 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - May 28 2001 |

### Fingerprint

### Keywords

- Complete graph
- Connected graph
- Edge-colouring
- r-uniform hypergraph

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*235*(1-3), 301-306. https://doi.org/10.1016/S0012-365X(00)00282-X

**Heredity properties of connectedness in edge-coloured complete graphs.** / Idzik, Adam; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 235, no. 1-3, pp. 301-306. https://doi.org/10.1016/S0012-365X(00)00282-X

}

TY - JOUR

T1 - Heredity properties of connectedness in edge-coloured complete graphs

AU - Idzik, Adam

AU - Tuza, Z.

PY - 2001/5/28

Y1 - 2001/5/28

N2 - If the monochromatic graphs G1 and G2 in a 2-edge-coloured complete graph Km (m ≥ 6) are connected, then there exist at least two vertices x such that the graphs G1\x and G2\x are also connected. Similar theorems are proved for k-edge-coloured complete graphs. They generalize earlier results of Idzik et al. [Discrete Math. 66 (1987) 119-125]. Examples are shown that analogous theorems are no longer true for 3-uniform complete hypergraphs.

AB - If the monochromatic graphs G1 and G2 in a 2-edge-coloured complete graph Km (m ≥ 6) are connected, then there exist at least two vertices x such that the graphs G1\x and G2\x are also connected. Similar theorems are proved for k-edge-coloured complete graphs. They generalize earlier results of Idzik et al. [Discrete Math. 66 (1987) 119-125]. Examples are shown that analogous theorems are no longer true for 3-uniform complete hypergraphs.

KW - Complete graph

KW - Connected graph

KW - Edge-colouring

KW - r-uniform hypergraph

UR - http://www.scopus.com/inward/record.url?scp=0035962815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035962815&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(00)00282-X

DO - 10.1016/S0012-365X(00)00282-X

M3 - Article

AN - SCOPUS:0035962815

VL - 235

SP - 301

EP - 306

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -