# Heavy subgraph pairs for traceability of block-chains

• Volume: 34, Issue: 2, page 287-307
• ISSN: 2083-5892

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## Abstract

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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

## How to cite

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Binlong Li, Hajo Broersma, and Shenggui Zhang. "Heavy subgraph pairs for traceability of block-chains." Discussiones Mathematicae Graph Theory 34.2 (2014): 287-307. <http://eudml.org/doc/268015>.

@article{BinlongLi2014,
abstract = {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},
author = {Binlong Li, Hajo Broersma, Shenggui Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {o−1-heavy subgraph; block-chain traceable graph; Ore-type condition; forbidden subgrap; -heavy subgraph; forbidden subgraph},
language = {eng},
number = {2},
pages = {287-307},
title = {Heavy subgraph pairs for traceability of block-chains},
url = {http://eudml.org/doc/268015},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Binlong Li
AU - Hajo Broersma
AU - Shenggui Zhang
TI - Heavy subgraph pairs for traceability of block-chains
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 2
SP - 287
EP - 307
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
LA - eng
KW - o−1-heavy subgraph; block-chain traceable graph; Ore-type condition; forbidden subgrap; -heavy subgraph; forbidden subgraph
UR - http://eudml.org/doc/268015
ER -

## References

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8. [8] H. Fleischner, The square of every two-connected graph is hamiltonian, J. Combin. Theory (B) 16 (1974) 29-34. doi:10.1016/0095-8956(74)90091-4[Crossref] Zbl0256.05121
9. [9] B. Li, H.J. Broersma and S. Zhang, Forbidden subgraph pairs for traceability of block-chains, Electron. J. Graph Theory Appl. 1 (2013) 1-10. Zbl1306.05205
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11. [11] B. Li and S. Zhang, On traceability of claw-o−1-heavy graphs (2013). arXiv:1303.0991v1

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