{"id":2354,"date":"2022-08-03T13:07:01","date_gmt":"2022-08-03T16:07:01","guid":{"rendered":"https:\/\/icc.fcen.uba.ar\/?p=2354"},"modified":"2022-08-03T13:07:01","modified_gmt":"2022-08-03T16:07:01","slug":"linear-time-algorithms-for-eliminating-claws-in-graphs","status":"publish","type":"post","link":"https:\/\/icc.fcen.uba.ar\/en\/linear-time-algorithms-for-eliminating-claws-in-graphs\/","title":{"rendered":"Linear-time Algorithms for Eliminating Claws in Graphs"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1144px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Authors: Flavia Bonomo-Braberman, Julliano R. Nascimento, Fabiano S. Oliveira, U\u00e9verton S. Souza, Jayme L. Szwarcfiter.<\/p>\n<p>Abstract:<br \/>\nSince many NP-complete graph problems have been shown polynomial-time solvable when restricted to claw-free graphs, we study the problem of determining the distance of a given graph to a claw-free graph, considering vertex elimination as measure. CLAW-FREE VERTEX DELETION (CFVD) consists of determining the minimum number of vertices to be removed from a graph such that the resulting graph is claw-free. Although CFVD is NP-complete in general and recognizing claw-free graphs is still a challenge, where the current best algorithm for a graph G has the same running time of the best algorithm for matrix multiplication, we present linear-time algorithms for CFVD on weighted block graphs and weighted graphs with bounded treewidth. Furthermore, we show that this problem can be solved in linear time by a simpler algorithm on forests, and we determine the exact values for full k-ary trees. On the other hand, we show that CLAW-FREE VERTEX DELETION is NP-complete even when the input graph is a split graph. We also show that the problem is hard to approximate within any constant factor better than 2, assuming the Unique Games Conjecture.<\/p>\n<p>More information:<br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2004.05672\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/arxiv.org\/abs\/2004.05672<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":2355,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[98],"tags":[],"class_list":["post-2354","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-papers"],"_links":{"self":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/comments?post=2354"}],"version-history":[{"count":1,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2354\/revisions"}],"predecessor-version":[{"id":2356,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2354\/revisions\/2356"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media\/2355"}],"wp:attachment":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media?parent=2354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/categories?post=2354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/tags?post=2354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}