From the 1 of 9 linked papers with an AI index.
9 papers
Excluding paths and bicliques
Maria Chudnovsky, Julien Codsi, Matjaž Krnc +1
The paper improves the known Ramsey‑type bound on the maximum length of a path in graphs that exclude a fixed path and a biclique as induced subgraphs, showing it can be taken sing…
Tree-independence number of -free graphs with no large bicliques
Václav Blažej, J. Pascal Gollin, Tomáš Hons +5
The tree-independence number of a graph is the minimum, over all tree-decompositions of the graph, of the maximum size of an independent set contained in a bag. Graph classes of bo…
Tree-independence number and forbidden induced subgraphs: excluding a -vertex path and a -biclique
Maria Chudnovsky, Julien Codsi, J. Pascal Gollin +2
We show that for every positive integer there exists an integer such that every graph that contains no induced subgraph isomorphic to either the -vertex path or…
Graph Classes Closed under Self-intersection
Konrad K. Dabrowski, Vadim V. Lozin, Martin MilaniÄ +3
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one o…
Closing paths to cycles in symmetric graphs
Martin MilaniÄ, ÄorÄe MitroviÄ
It was shown by Beisegel, Chudnovsky, Gurvich, MilaniÄ, and Servatius in 2022 that every induced -edge path in a vertex-transitive graph closes to an induced cycle. Similar res…
Computing Tree Decompositions with Small Independence Number
Clément Dallard, Fedor V. Fomin, Petr A. Golovach +2
The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the mini…