Product structure of graph classes with bounded treewidth
Product structure of graph classes with bounded treewidth Page 1 Combinatorics, Probability
and Computing (2023), 1–26 doi:10.1017/S0963548323000457 ARTICLE Product structure of …
and Computing (2023), 1–26 doi:10.1017/S0963548323000457 ARTICLE Product structure of …
Rolling backwards can move you forward: on embedding problems in sparse expanders
We develop a general embedding method based on the Friedman-Pippenger tree
embedding technique and its algorithmic version, enhanced with a roll-back idea allowing a …
embedding technique and its algorithmic version, enhanced with a roll-back idea allowing a …
Tree-partitions with bounded degree trees
M Distel, DR Wood - 2021-2022 MATRIX Annals, 2024 - Springer
A tree-partition of a graph G is a partition of V (G) such that identifying the vertices in each
part gives a tree. It is known that every graph with treewidth k and maximum degree Δ has a …
part gives a tree. It is known that every graph with treewidth k and maximum degree Δ has a …
The size‐Ramsey number of powers of bounded degree trees
S Berger, Y Kohayakawa, GS Maesaka… - Journal of the …, 2021 - Wiley Online Library
Given a positive integer s, the s‐colour size‐Ramsey number of a graph H is the smallest
integer m such that there exists a graph G with m edges with the property that, in any …
integer m such that there exists a graph G with m edges with the property that, in any …
Size-Ramsey numbers of structurally sparse graphs
N Draganić, M Kaufmann, DM Correia… - arXiv preprint arXiv …, 2023 - arxiv.org
Size-Ramsey numbers are a central notion in combinatorics and have been widely studied
since their introduction by Erd\H {o} s, Faudree, Rousseau and Schelp in 1978. Research …
since their introduction by Erd\H {o} s, Faudree, Rousseau and Schelp in 1978. Research …
Size-Ramsey numbers of graphs with maximum degree three
N Draganić, K Petrova - arXiv preprint arXiv:2207.05048, 2022 - arxiv.org
The size-Ramsey number $\hat {r}(H) $ of a graph $ H $ is the smallest number of edges a
(host) graph $ G $ can have, such that for any red/blue colouring of $ G $, there is a …
(host) graph $ G $ can have, such that for any red/blue colouring of $ G $, there is a …
[PDF][PDF] Embedding induced trees in sparse expanding graphs
Inspired by the network routing literature\cite {aggarwal1996efficient}, we develop what we
call a``Pre-Emptive Greedy Algorithm" to embed bounded degree induced trees in sparse …
call a``Pre-Emptive Greedy Algorithm" to embed bounded degree induced trees in sparse …
Size-Ramsey numbers of powers of hypergraph trees and long subdivisions
S Letzter, A Pokrovskiy, L Yepremyan - arXiv preprint arXiv:2103.01942, 2021 - arxiv.org
The $ s $-colour size-Ramsey number of a hypergraph $ H $ is the minimum number of
edges in a hypergraph $ G $ whose every $ s $-edge-colouring contains a monochromatic …
edges in a hypergraph $ G $ whose every $ s $-edge-colouring contains a monochromatic …
Effective bounds for induced size-Ramsey numbers of cycles
The induced size-Ramsey number\(\hat {r} _\text {ind}^ k (H)\) of a graph H is the smallest
number of edges a (host) graph G can have such that for any k-coloring of its edges, there …
number of edges a (host) graph G can have such that for any k-coloring of its edges, there …
Induced Ramsey problems for trees and graphs with bounded treewidth
Z Hunter, B Sudakov - arXiv preprint arXiv:2406.00352, 2024 - arxiv.org
The induced $ q $-color size-Ramsey number $\hat {r} _ {\text {ind}}(H; q) $ of a graph $ H $
is the minimal number of edges a host graph $ G $ can have so that every $ q $-edge …
is the minimal number of edges a host graph $ G $ can have so that every $ q $-edge …