Results 81 to 90 of about 8,313 (308)
Exact Algorithm for the Maximum Induced Planar Subgraph Problem
, 2011 International audienceWe prove that in an n-vertex graph, an induced planar subgraph of maximum size can be found in time O(1.7347^n ). This is the first algorithm breaking the trivial 2^n n^{O(1)} bound of the brute-force search algorithm for the ...
Yngve Villanger +5 more
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On matroids induced by packing subgraphs
Journal of Combinatorial Theory, Series B, 1988 The class of those connected graphs H is described such that in any graph the vertex set covered by vertex disjoint copies of H and edges form the independent sets of a matroid. The condition is that H is either critical or has a 1-factor, or, finally, it has a degree-one vertex and a vertex c such that for every \(x\neq c\), H-x has a 1-factor.
Martin Loebl, Svatopluk Poljak
openaire +1 more source
Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley +1 more source
Forbidden substructures: induced subgraphs, Ramsey games, and sparse hypergraphs [PDF]
, 2012 We study problems in extremal combinatorics with respect to forbidden induced subgraphs, forbidden colored subgraphs, and forbidden subgraphs. In Chapter 2, we determine exactly which graphs H have the property that almost every H-free graph has a vertex
Butterfield, Jane
core
Maximum triangle-free induced subgraph
, 2019 A clever idea is frequently necessarily the key to solve mathematics problems from Prasolov books. Modern mathematics, especially the theory of NP-completeness starting from the classical book of [1], also gradually moves forward similarly.
Thinh D. Nguyen (6385907)
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Halin's Grid Theorem for Digraphs
Journal of Graph Theory, EarlyView.ABSTRACT Halin showed that every thick end of every graph contains an infinite grid. We extend Halin's theorem to digraphs. More precisely, we show that for every infinite family ℛ ${\rm{ {\mathcal R} }}$ of disjoint equivalent out‐rays there is a grid whose vertical rays are contained in ℛ ${\rm{ {\mathcal R} }}$.
Florian Reich
wiley +1 more source
Subgraph Queries by Context-free Grammars
Journal of Integrative Bioinformatics, 2008 We describe a method for querying vertex- and edge-labeled graphs using context-free grammars to specify the class of interesting paths. We introduce a novel problem, finding the connection subgraph induced by the set of matching paths between given two ...
Sevon Petteri, Eronen Lauri
doaj +1 more source
The maximum happy induced subgraph problem: Bounds and algorithms
, 2021 The maximum happy induced subgraph problem: Bounds and ...
Dhananjay Thiruvady (13066857) +2 more
core
Large Nearly Regular Induced Subgraphs [PDF]
SIAM Journal on Discrete Mathematics, 2008 For a real c \geq 1 and an integer n, let f(n,c) denote the maximum integer f so that every graph on n vertices contains an induced subgraph on at least f vertices in which the maximum degree is at most c times the minimum degree. Thus, in particular, every graph on n vertices contains a regular induced subgraph on at least f(n,1) vertices. The problem
Noga Alon +2 more
openaire +2 more sources
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source