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      <title>Complexity of finding maximal color-avoiding connected subgraphs</title>
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      <abstractText>Two vertices of a (not necessarily properly) vertex-colored digraph are called vertex-ℓ-
color-avoiding strongly k-arc-connected if, after the removal of the vertices of any at most
ℓ colors, either at least one of the two vertices is removed, or they remain strongly k-arc-
connected. The vertex-ℓ-color-avoiding strongly k-arc-connected components are maximal sets of vertices such that any two vertex belonging to the set is vertex-ℓ-color-avoiding strongly k-arc-connected in the graph.
We show that finding these components is NP-hard in general, but this problem be-
comes solvable in polynomial time when each vertex is single-colored. We also investigate the problem of finding the maximal vertex-ℓ-color-avoiding strongly k-arc-connected sub-graphs. We prove that this problem is likewise NP-hard in general but becomes solvable in polynomial time when each vertex is single-colored. In addition, we explore possible generalizations to k-vertex-connectivity and to arc-colored digraphs.</abstractText>
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adattudomány, hálózattudomány&lt;/span&gt;) &lt;/a&gt; &lt;/span&gt; &lt;span class=&quot;author-affil&quot;&gt;&lt;span title=&quot;Budapesti Műszaki és Gazdaságtudományi Egyetem&quot;&gt;BME&lt;/span&gt;/&lt;span title=&quot;Természettudományi Kar&quot;&gt;TTK&lt;/span&gt;/&lt;span title=&quot;Matematika Intézet&quot;&gt;MI&lt;/span&gt;/Sztochasztika Tanszék&lt;/span&gt; ;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;span class=&quot;author-name&quot; mtid=&quot;10051898&quot;&gt;&lt;a href=&quot;/gui2/?type=authors&amp;mode=browse&amp;sel=10051898&quot; target=&quot;_blank&quot;&gt;Varga Kitti (&lt;span class=&quot;authorship-author-name&quot;&gt;Varga Kitti Katalin&lt;/span&gt; &lt;span class=&quot;authorAux-mtmt&quot;&gt; számítástudomány&lt;/span&gt;) &lt;/a&gt; &lt;/span&gt; &lt;span class=&quot;author-affil&quot;&gt;&lt;span title=&quot;Budapesti Műszaki és Gazdaságtudományi Egyetem&quot;&gt;BME&lt;/span&gt;/&lt;span title=&quot;Villamosmérnöki és Informatikai Kar&quot;&gt;VIK&lt;/span&gt;/Számítástudományi és Információelméleti Tanszék; &lt;span title=&quot;Eötvös Loránd Tudományegyetem&quot;&gt;ELTE&lt;/span&gt;/&lt;span title=&quot;Természettudományi Kar&quot;&gt;TTK&lt;/span&gt;/&lt;span title=&quot;Matematikai Intézet&quot;&gt;Mat_I&lt;/span&gt;/HUN-REN-ELTE Egerváry Jenő Kombinatorikus Optimalizálási Kutatócsoport&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&quot;title&quot;&gt;&lt;a href=&quot;/gui2/?mode=browse&amp;params=publication;36432650&quot; target=&quot;_blank&quot;&gt;Complexity of finding maximal color-avoiding connected subgraphs&lt;/a&gt;&lt;/div&gt; &lt;div class=&quot;InBook&quot;&gt;&lt;div class=&quot;chapter-in&quot;&gt;In:&lt;/div&gt; &lt;div class=&quot;authors&quot;&gt; &lt;/div&gt; &lt;div class=&quot;booktitle&quot;&gt;&lt;a href=&quot;/gui2/?mode=browse&amp;params=publication;36432641&quot; target=&quot;_blank&quot;&gt;EUROCOMB&apos;25 : Booklet of extended abstracts &lt;/a&gt;&lt;/div&gt; &lt;div class=&quot;conference&quot;&gt; Konferencia helye, ideje: &lt;span class=&quot;location&quot;&gt;Budapest, Magyarország &lt;span class=&quot;conference-date&quot;&gt;2025.08.25. - 2025.08.29.&lt;/span&gt; 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