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Induced subgraphs and tree decompositions XIII. Basic obstructions in -free graphs for finite
Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi +1
Unlike minors, the induced subgraph obstructions to bounded treewidth come in a large variety, including, for every , the -basic obstructions: the graphs and…
Induced subgraphs and tree decompositions XII. Grid theorem for pinched graphs
Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi +1
Given an integer , we say a graph is -pinched if does not contain an induced subgraph consisting of cycles, all going through a single common vertex…
Induced subgraphs and tree decompositions XI. Local structure in even-hole-free graphs of large treewidth
Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi +1
We prove a conjecture of Sintiari and Trotignon that every even-hole-free graph of sufficiently large treewidth contains a four-vertex induced subgraph with at least five edges (th…
Induced subgraphs and tree decompositions X. Towards logarithmic treewidth for even-hole-free graphs
Tara Abrishami, Bogdan Alecu, Maria Chudnovsky +2
A generalized -pyramid is a graph obtained from a certain kind of tree (a subdivided star or a subdivided cubic caterpillar) and the line graph of a subdivided cubic caterpillar…
Tree independence number I. (Even hole, diamond, pyramid)-free graphs
Tara Abrishami, Bogdan Alecu, Maria Chudnovsky +3
The tree-independence number tree-, first defined and studied by Dallard, Milanič and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem.…
Induced subgraphs and tree decompositions IX. Grid theorem for perforated graphs
Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi +1
The celebrated Erdős-Pósa Theorem, in one formulation, asserts that for every , graphs with no subgraph (or equivalently, minor) isomorphic to the disjoint union of cy…
Induced subgraphs and tree decompositions VIII. Excluding a forest in (theta, prism)-free graphs
Tara Abrishami, Bogdan Alecu, Maria Chudnovsky +2
Given a graph , we prove that every (theta, prism)-free graph of sufficiently large treewidth contains either a large clique or an induced subgraph isomorphic to , if and onl…