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The strong perfect graph theorem [PDF]
Annals of Mathematics, 2006 A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The "strong perfect graph conjecture" (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A
Robin Thomas +3 more
semanticscholar +8 more sources
Anticoncentration of Random Vectors via the Strong Perfect Graph Theorem
Combinatorica, 2023 In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (1994) and a question of Jones (1978). The highlight of this work is an application of the strong perfect graph theorem by Chudnovsky, Robertson ...
Juškevičius, Tomas +1 more
semanticscholar +6 more sources
A semi-strong Perfect Graph theorem
Journal of Combinatorial Theory, Series B, 1987 The perfectness of a graph G was defined by Berge in 1961. He also proposed the following two conjectures: (1) G is perfect if and only if it contains no induced subgraph isomorphic to an odd cycle of length greater than three or the complement of such a cycle (strong perfect graph conjecture) and (2) G is perfect if and only if \(\bar G\) is perfect ...
Bruce Reed
semanticscholar +5 more sources
The strong perfect graph theorem [PDF]
100 Years of Math Milestones, 2019 In 1960 Berge came up with the concept of perfect graphs, and in doing so, conjectured some characteristics about them. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that ...
Stephan Ramon Garcia, Steven Miller
semanticscholar +3 more sources
Note on Perfect Forests in Digraphs [PDF]
Journal of Graph Theory, 2015 A spanning subgraph $F$ of a graph $G$ is called {\em perfect} if $F$ is a forest, the degree $d_F(x)$ of each vertex $x$ in $F$ is odd, and each tree of $F$ is an induced subgraph of $G$.
Bang-Jensen, Gutin, Scott
core +4 more sources
Clique-Stable Set separation in perfect graphs with no balanced skew-partitions [PDF]
, 2016 Inspired by a question of Yannakakis on the Vertex Packing polytope of perfect graphs, we study the Clique-Stable Set Separation in a non-hereditary subclass of perfect graphs.
Lagoutte, Aurélie, Trunck, Théophile
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On Perfectness of Intersection Graph of Ideals of ℤn
Discussiones Mathematicae - General Algebra and Applications, 2017 In this short paper, we characterize the positive integers n for which intersection graph of ideals of ℤn is perfect.
Das Angsuman
doaj +1 more source
Interdiction Problems on Planar Graphs [PDF]
, 2013 Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded graph. We introduce
Pan, Feng, Schild, Aaron
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Strong Integer Additive Set-valued Graphs: A Creative Review [PDF]
, 2015 For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $
K. A. Germina +3 more
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Disjoint Dominating Sets with a Perfect Matching
, 2017 In this paper, we consider dominating sets $D$ and $D'$ such that $D$ and $D'$ are disjoint and there exists a perfect matching between them. Let $DD_{\textrm{m}}(G)$ denote the cardinality of smallest such sets $D, D'$ in $G$ (provided they exist ...
Ayello, Alejandro Angeli +2 more
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