Results 51 to 60 of about 9,740 (155)
Problems in extremal graph theory [PDF]
, 2010 We consider a variety of problems in extremal graph and set theory. The {\em chromatic number} of $G$, $\chi(G)$, is the smallest integer $k$ such that $G$ is $k$-colorable.
Ozkahya, Lale
core
Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph G = ( V , E , w ) $G=(V,E,w)$ has a bisection with weight at least θ ⋅ w (
Stefanie Gerke +3 more
wiley +1 more source
Forbidden subgraphs, stability and hamiltonicity
Discrete Mathematics, 1999 The authors study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in \textit{Z. Ryjáček} [J. Comb. Theory, Ser. B 70, No.~2, 217-224 (1997; Zbl 0872.05032)]. They characterize all connected graphs \(A\) such that the class of all \(CA\)-free graphs (where \(C\) denotes the ...
Jan Brousek +2 more
openaire +1 more source
A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2
Algorithms, 2021 Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of
Serafino Cicerone
doaj +1 more source
Pairwise Imitation and Tournament Graphs
International Economic Review, EarlyView.ABSTRACT This paper investigates strategic dynamics under the behavioral rule of pairwise interact and imitate (PII), which requires minimal information and emphasizes outperforming opponents in pairwise interactions. We characterize PII using weak tournament graphs and, for a broad class of dynamics, establish a one‐shot stability result for ...
Sung‐Ha Hwang +3 more
wiley +1 more source
Forbidden subgraphs and the Kőnig property
Electronic Notes in Discrete Mathematics, 2011 Abstract A graph has the Kőnig property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Kőnig property by forbidden subgraphs, restricted to graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszʼs result to a characterization of all graphs having the Kőnig ...
Mitre Costa Dourado +4 more
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On the 12-Representability of Induced Subgraphs of a Grid Graph
Discussiones Mathematicae Graph Theory, 2022 The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
doaj +1 more source
Heavy subgraphs, stability and hamiltonicity
, 2016 Let $G$ be a graph. Adopting the terminology of Broersma et al. and \v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every
Li, Binlong, Ning, Bo
core +2 more sources
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
The Largest Subgraph Without A Forbidden Induced Subgraph
Combinatorica20 ...
Jacob Fox, Rajko Nenadov, Huy Tuan Pham
openaire +2 more sources