Results 81 to 90 of about 5,860 (222)
Tree-width and large grid minors in planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Graphs and ...
Alexander Grigoriev
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Mathematics, 2023 Considering the worst-case scenario, the junction-tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees.
Alexander Bauer +2 more
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Super stable tensegrities and the Colin de Verdière number ν
Journal of Graph Theory, Volume 108, Issue 3, Page 401-431, March 2025.Abstract A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars and struts connected by cables with tension. We introduce the super stability number of a multigraph as the maximum dimension that a multigraph can be realized as a super stable tensegrity, and show that it equals the Colin de ...
Ryoshun Oba, Shin‐ichi Tanigawa
wiley +1 more source
Size‐Ramsey numbers of graphs with maximum degree three
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract The size‐Ramsey number r̂(H)$\hat{r}(H)$ of a graph H$H$ is the smallest number of edges a (host) graph G$G$ can have, such that for any red/blue colouring of G$G$, there is a monochromatic copy of H$H$ in G$G$. Recently, Conlon, Nenadov and Trujić showed that if H$H$ is a graph on n$n$ vertices and maximum degree three, then r̂(H)=O(n8/5 ...
Nemanja Draganić, Kalina Petrova
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Graph limits of random graphs from a subset of connected k‐trees
Random Structures &Algorithms, Volume 55, Issue 1, Page 125-152, August 2019., 2019 For any set Ω of non‐negative integers such that , we consider a random Ω‐k‐tree Gn,k that is uniformly selected from all connected k‐trees of (n + k) vertices such that the number of (k + 1)‐cliques that contain any fixed k‐clique belongs to Ω. We prove that Gn,k, scaled by where Hk is the kth harmonic number and σΩ > 0, converges to the continuum ...
Michael Drmota +2 more
wiley +1 more source
Journal of Graph Theory, Volume 106, Issue 4, Page 816-842, August 2024.Abstract A minimal separator of a graph G is a set S ⊆ V ( G ) such that there exist vertices a , b ∈ V ( G ) ⧹ S with the property that S separates a from b in G, but no proper subset of S does. For an integer k ≥ 0, we say that a minimal separator is k‐simplicial if it can be covered by k cliques and denote by G k the class of all graphs in which ...
Martin Milanič +3 more
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Subcubic graphs of large treewidth do not have the edge-Erdős-Pósa property [PDF]
arXiv, 2023 We show that subcubic graphs of treewidth at least $2500$ do not have the edge-Erd\H{o}s-P\'{o}sa property.
arxiv
Tree independence number I. (Even hole, diamond, pyramid)‐free graphs
Journal of Graph Theory, Volume 106, Issue 4, Page 923-943, August 2024.Abstract The tree‐independence number tree‐ α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so‐called central bag method to study induced obstructions to bounded treewidth.
Tara Abrishami +5 more
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A more accurate view of the Flat Wall Theorem
Journal of Graph Theory, Volume 107, Issue 2, Page 263-297, October 2024.Abstract We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in flat walls.
Ignasi Sau +2 more
wiley +1 more source
On the parameterized complexity of computing tree-partitions [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree.
Hans L. Bodlaender +2 more
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