Two-Coloring the Edges of a Cubic Graph Such That Each Monochromatic Component Is a Path of Length at Most 5

Carsten Thomassen
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
We prove the conjecture made by Bermond, Fouquet, Habib, and Pe roche in 1984 that every cubic graph has an edge-coloring as described in the title. The number 5 cannot be replaced by 4.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jctb.1998.1868">doi:10.1006/jctb.1998.1868</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s5u3ggdzyrg6jbudvlughbix7e">fatcat:s5u3ggdzyrg6jbudvlughbix7e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190418214548/https://core.ac.uk/download/pdf/82315392.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/f9/8c/f98c4d2eb1b3c40c03edee226208fbfb2dba05df.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jctb.1998.1868"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>