Cubic graphs with large circumference deficit [article]

Edita Máčajová, Ján Mazák
<span title="2013-11-09">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The circumference c(G) of a graph G is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically 4-, 5- and 6-edge-connected cubic graphs with circumference ratio c(G)/|V(G)| bounded from above by 0.876, 0.960 and 0.990, respectively. In contrast, the dominating cycle conjecture implies that the circumference ratio of a cyclically 4-edge-connected cubic graph is at least 0.75. In addition, we construct snarks with large
more &raquo; ... irth and large circumference deficit, solving Problem 1 proposed in [J. Hägglund and K. Markström, On stable cycles and cycle double covers of graphs with large circumference, Disc. Math. 312 (2012), 2540--2544].
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.1042v2">arXiv:1310.1042v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/trxtlyy67fhdxlvpw4tsjt2xve">fatcat:trxtlyy67fhdxlvpw4tsjt2xve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191018032150/https://arxiv.org/pdf/1310.1042v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/37/72/37720a3bd095d7105fe82e991c3b5aa05c20d5c1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.1042v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>