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
@article{bwmeta1.element.doi-10_7151_dmgt_1737,
author = {Binlong Li and Hajo Broersma and Shenggui Zhang},
title = {Heavy subgraph pairs for traceability of block-chains},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {287-307},
zbl = {1290.05099},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1737}
}
Binlong Li; Hajo Broersma; Shenggui Zhang. Heavy subgraph pairs for traceability of block-chains. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 287-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1737/
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