Peter Gartland

activity

20182024

most citedFinding large induced sparse subgraphs in

C_{> t}

-free graphs in quasipolynomial time

6 citations · 16 across the 5 of their papers we have counts for

collaborators

8 papers

math.CO2024

Tree Independence Number IV. Even-hole-free Graphs

Maria Chudnovsky, Peter Gartland, Sepehr Hajebi +2

We prove that the tree independence number of every even-hole-free graph is at most polylogarithmic in its number of vertices. More explicitly, we prove that there exists a constan…

math.CO2024

Induced subgraphs and tree decompositions XV. Even-hole-free graphs with bounded clique number have logarithmic treewidth

Maria Chudnovsky, Peter Gartland, Sepehr Hajebi +2

We prove that for every integer $t \geq 1$ there exists an integer $c_{t} \geq 1$ such that every $n$ -vertex even-hole-free graph with no clique of size $t$ has treewidth at most $c_t\…

math.CO2023

On Induced Versions of Menger's Theorem on Sparse Graphs

Peter Gartland, Tuukka Korhonen, Daniel Lokshtanov

Let $A$ and $B$ be sets of vertices in a graph $G$ . Menger's theorem states that for every positive integer $k$ , either there exists a collection of $k$ vertex-disjoint paths betwe…

cs.DS2023★ 5 cited

Maximum Weight Independent Set in Graphs with no Long Claws in Quasi-Polynomial Time

Peter Gartland, Daniel Lokshtanov, Tomáš Masařík +3

We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-polynomial time on $H$ -free graphs (graphs excluding a fixed graph $H$ as an induced subgraph)…

cs.DM2020

Dominated Minimal Separators are Tame (Nearly All Others are Feral)

Peter Gartland, Daniel Lokshtanov

A class $F$ of graphs is called {\em tame} if there exists a constant $k$ so that every graph in $F$ on $n$ vertices contains at most $O (n^{k})$ minimal separators, {\e…

cs.DS2020★ 6 cited

Finding large induced sparse subgraphs in $C_{> t}$ -free graphs in quasipolynomial time

Peter Gartland, Daniel Lokshtanov, Marcin Pilipczuk +2

For an integer $t$ , a graph $G$ is called {\em{ $C_{> t}$ -free}} if $G$ does not contain any induced cycle on more than~ $t$ vertices. We prove the following statement: for every pair…

cs.DS2020★ 5 cited

Independent Set on P $_{k}$ -Free Graphs in Quasi-Polynomial Time

Peter Gartland, Daniel Lokshtanov

We present an algorithm that takes as input a graph $G$ with weights on the vertices, and computes a maximum weight independent set $S$ of $G$ . If the input graph $G$ excludes a pa…

math.CO2018

A New Characterization of $V$ -Posets

Joshua Cooper, Peter Gartland, Hays Whitlatch

In 2016, Hasebe and Tsujie gave a recursive characterization of the set of induced $N$ -free and bowtie-free posets; Misanantenaina and Wagner studied these orders further, naming t…