Results 141 to 150 of about 5,057 (262)
Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness. [PDF]
Algorithmica, 2020 Roth M, Schmitt J.
europepmc +1 more source
Testing whether a digraph contains H-free k-induced subgraphs
, 2008 A subgraph induced by k vertices is called a k-induced subgraph. We prove that determining if a digraph G contains H-free k-induced subgraphs is Ω(N2)-evasive. Then we construct an ϵ-tester to test this property.
Ma, Tak-Man +7 more
core +1 more source
Long Induced Paths in K s , s‐Free Graphs
Journal of Graph Theory, Volume 112, Issue 4, Page 438-441, August 2026.ABSTRACT More than 40 years ago, Galvin, Rival, and Sands showed that every K s , s‐free graph containing an n‐vertex path must contain an induced path of length f ( n ), where f ( n ) → ∞ as n → ∞. Recently, it was shown by Duron, Esperet, and Raymond that one can take f ( n ) = ( log log n ) 1 / 5 − o ( 1 ).
Zach Hunter +3 more
wiley +1 more source
Some problems on induced subgraphs
Discrete Applied Mathematics, 2018 We discuss some problems related to induced subgraphs. The first problem is about getting a good upper bound for the chromatic number in terms of the clique number for graphs in which every induced cycle has length $3$ or $4$. The second problem is about the perfect chromatic number of a graph, which is the smallest number of perfect sets into which ...
openaire +4 more sources
On Oriented Colourings of Graphs on Surfaces
Journal of Graph Theory, Volume 112, Issue 4, Page 357-369, August 2026.ABSTRACT For an oriented graph G, the least number of colours required to oriented colour G is called the oriented chromatic number of G and denoted χ o ( G ). For a non‐negative integer g let χ o ( g ) be the least integer such that χ o ( G ) ≤ χ o ( g ) for every oriented graph G with Euler genus at most g.
Alexander Clow
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Edge‐Length Preserving Embeddings of Graphs Between Normed Spaces
Journal of Graph Theory, Volume 112, Issue 4, Page 491-506, August 2026.ABSTRACT The concept of graph embeddability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph G = ( V , E ) is said to be ( X , Y )‐embeddable if any set of induced edge lengths from an embedding of G into a ...
Sean Dewar +3 more
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A Note on Lower Bounds for Induced Ramsey Numbers
Discussiones Mathematicae Graph Theory, 2019 We say that a graph F strongly arrows a pair of graphs (G,H) and write F →ind$\mathop \to \limits^{{\rm{ind}}} $(G,H) if any 2-coloring of its edges with red and blue leads to either a red G or a blue H appearing as induced subgraphs of F.
Gorgol Izolda
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Journal of Graph Theory, Volume 112, Issue 3, Page 198-208, July 2026.ABSTRACT We prove that the Ramsey number R ( 5 , 5 ) is less than or equal to 46. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computational parts of the proof were independently implemented by both authors, with consistent results.
Vigleik Angeltveit, Brendan D. McKay
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New graph classes characterized by weak vertex separators and two-pairs
AKCE International Journal of Graphs and Combinatorics, 2017 A set of vertices whose deletion from a graph would increase the distance between two remaining vertices is called a weak vertex separator of the graph. Two vertices form a two-pair if all chordless paths between them have length .
Terry A. McKee
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Towards Characterization of Five‐List‐Colorability of Toroidal Graphs
Journal of Graph Theory, Volume 112, Issue 3, Page 267-275, July 2026.ABSTRACT Through computer‐assisted enumeration, we list minimal obstructions for 5‐choosability of graphs on the torus with the following additional property: There exists a cyclic system of non‐contractible triangles around the torus where the consecutive triangles are at distance at most four.
Zdeněk Dvořák +1 more
wiley +1 more source