Document Zbl 1302.05148

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Comb. Theory, Ser. B</a> <a href="/?q=in%3A338596" title="Articles in this Issue">110, 47-66 (2015)</a>. </div> <div class="abstract">Summary: We present an easy structure theorem for graphs which do not admit an immersion of the complete graph $K_t$. The theorem motivates the definition of a variation of tree decompositions based on edge cuts instead of vertex cuts which we call tree-cut decompositions. We give a definition for the width of tree-cut decompositions, and using this definition along with the structure theorem for excluded clique immersions, we prove that every graph either has bounded tree-cut width or admits an immersion of a large wall.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6371811">Cited in <strong>5</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A6371811">Cited in <strong>43</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C70" title="MSC2020">05C70</a> </td> <td class="space"> Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C05" title="MSC2020">05C05</a> </td> <td class="space"> Trees </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aimmersion">immersion</a>; <a href="/?q=ut%3Aedge+disjointness">edge disjointness</a>; <a href="/?q=ut%3Atree+decompositions">tree decompositions</a>; <a href="/?q=ut%3Atree-cut+decompositions">tree-cut decompositions</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1302.05148" data-ciurl="/ci/06371811" data-biburl="/bibtex/06371811.bib" data-amsurl="/amsrefs/06371811.bib" data-xmlurl="/xml/06371811.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06371811.pdf" title="Zbl 1302.05148 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.jctb.2014.07.003" aria-label="DOI for “The structure of graphs not admitting a fixed immersion”" title="10.1016/j.jctb.2014.07.003">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1302.3867"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abu-Khzam, F.; Langston, M., Graph coloring and the immersion order, (Lecture Notes in Comput. 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D.; Thomas, R., Call routing and the ratcatcher, Combinatorica, 14, 2, 217-241 (1994) · <a href="/0799.05057" class="nowrap">Zbl 0799.05057</a></td> </tr><tr> <td>[20]</td> <td class="space">Thilikos, D. M.; Serna, M.; Bodlaender, H. L., Cutwidth I: a linear time fixed parameter algorithm, J. Algorithms, 56, 1, 1-24 (2005) · <a href="/1161.68856" class="nowrap">Zbl 1161.68856</a></td> </tr><tr> <td>[21]</td> <td class="space">Thilikos, D. M.; Serna, M.; Bodlaender, H. L., Cutwidth II: algorithms for partial w-trees of bounded degree, J. Algorithms, 56, 1, 25-49 (2005) · <a href="/1161.68857" class="nowrap">Zbl 1161.68857</a></td> </tr><tr> <td>[22]</td> <td class="space">Yannakakis, M., A polynomial algorithm for the min-cut linear arrangement of trees, J. 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