### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 287-307 |

Number of pages | 21 |

Journal | Discussiones mathematicae. Graph theory |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- MSC-05C07
- MSC-05C38
- MSC-05C45
- EWI-24776
- Traceable graph
- IR-91190
- $o_{-1}$-Heavy subgraph
- Block-chain
- Forbidden subgraph
- METIS-304107
- Ore-type condition

### Cite this

*Discussiones mathematicae. Graph theory*,

*34*(2), 287-307. https://doi.org/10.7151/dmgt.1737

}

*Discussiones mathematicae. Graph theory*, vol. 34, no. 2, pp. 287-307. https://doi.org/10.7151/dmgt.1737

**Heavy subgraph pairs for traceability of block-chains.** / Li, Binlong; Li, Binlong; Broersma, Haitze J.; Zhang, Shenggui.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Heavy subgraph pairs for traceability of block-chains

AU - Li, Binlong

AU - Li, Binlong

AU - Broersma, Haitze J.

AU - Zhang, Shenggui

N1 - eemcs-eprint-24776

PY - 2014

Y1 - 2014

N2 - A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o-1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two end-blocks. Obviously, every traceable graph is a block-chain, but the reverse does not hold. In this paper we characterize all the pairs of connected o-1-heavy graphs that guarantee traceability of block-chains. Our main result is a common extension of earlier work on degree sum conditions, forbidden subgraph conditions and heavy subgraph conditions for traceability.

AB - A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o-1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two end-blocks. Obviously, every traceable graph is a block-chain, but the reverse does not hold. In this paper we characterize all the pairs of connected o-1-heavy graphs that guarantee traceability of block-chains. Our main result is a common extension of earlier work on degree sum conditions, forbidden subgraph conditions and heavy subgraph conditions for traceability.

KW - MSC-05C07

KW - MSC-05C38

KW - MSC-05C45

KW - EWI-24776

KW - Traceable graph

KW - IR-91190

KW - $o_{-1}$-Heavy subgraph

KW - Block-chain

KW - Forbidden subgraph

KW - METIS-304107

KW - Ore-type condition

U2 - 10.7151/dmgt.1737

DO - 10.7151/dmgt.1737

M3 - Article

VL - 34

SP - 287

EP - 307

JO - Discussiones mathematicae. Graph theory

JF - Discussiones mathematicae. Graph theory

SN - 1234-3099

IS - 2

ER -