
1by Łuczak, Tomasz Polcyn, Joanna Reiher, Christian Published in Journal of graph theory (01.09.2021)“...Given positive integers n ⩾ s, we let ex ( n , s ) denote the maximum number of edges in a triangle‐free graph G on n vertices with α ( G ) ⩽ s. In the early...”

2by Bernshteyn, Anton Published in Random structures & algorithms (01.07.2019)“...The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for...”

3by Davies, Ewan De Joannis de Verclos, R Kang, R.J Pirot, F Published in Random structures & algorithms (2020)“...We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of...”

4by Dvořák, Zdeněk Král', Daniel Thomas, Robin Published in Journal of combinatorial theory. Series B (01.09.2021)“...We settle a problem of Havel by showing that there exists an absolute constant d such that if G is a planar graph in which every two distinct triangles are at...”

5“...The smallest number of cliques, covering all edges of a graph G, is called the (edge) clique cover number of G and is denoted by cc(G). It is an easy...”

6by Bedenknecht, Wiebke Mota, Guilherme Oliveira Reiher, Christian Schacht, Mathias Published in Journal of graph theory (01.02.2019)“...Erdős conjectured that every n‐vertex triangle‐free graph contains a subset of ⌊n/2⌋ vertices that spans at most n2/50 edges. Extending a recent result of...”

7“...The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum...”

8“...The theory of Dvořák, Král', and Thomas [Dvořák, Z., D. Král', and R. Thomas, Threecoloring trianglefree graphs on surfaces IV. Bounding face sizes of...”

9by Basavaraju, Manu Heggernes, Pinar van ′t Hof, Pim Saei, Reza Villanger, Yngve Published in Journal of graph theory (01.11.2016)“...An induced matching in a graph is a set of edges whose endpoints induce a 1‐regular subgraph. It is known that every n‐vertex graph has at most 10n/5≈1.5849n...”

10by Bernshteyn, Anton Published in Discrete mathematics (06.11.2016)“...Alon (2000) proved that for any graph G, χℓ(G)=Ω(lnd), where χℓ(G) is the list chromatic number of G and d is the average degree of G. Dvořák and Postle (2015)...”

11by Mosca, Raffaele Published in Graphs and combinatorics (02.06.2021)“...AbstractThe Maximum Weight Independent Set Problem (WIS) is a wellknown NPhard problem. A popular way to study WIS is to detect graph classes for which WIS...”

12by Bohman, Tom Frieze, Alan Lubetzky, Eyal Published in Advances in mathematics (New York. 1965) (06.08.2015)“...Starting from a complete graph on n vertices, repeatedly delete the edges of a uniformly chosen triangle. This stochastic process terminates once it arrives at...”

13by Cameron, Peter J Dang, Anh N Riis, Søren Published in The Electronic journal of combinatorics (18.03.2016)“...The guessing game introduced by Riis [Electron. J. Combin. 2007] is a variant of the "guessing your own hats" game and can be played on any simple directed...”

14“...For c∈Q∗, let φc:Q→Q denote the quadratic map φc(X)=X2+c. How large can the period of a rational periodic point of φc be? Poonen conjectured that it cannot...”

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16by Gruber, Alexander Keller, Thomas Michael Lewis, Mark L Naughton, Keeley Strasser, Benjamin Published in Journal of algebra (01.11.2015)“...Byline: Alexander Gruber, Thomas Michael Keller, Mark L. Lewis, Keeley Naughton, Benjamin Strasser Let [pi](G) denote the set of prime divisors of the order of...”

17“...In this paper, we study a dynamic coloring of the vertices of a graph G that starts with an initial subset S of colored vertices, with all remaining vertices...”

18by Postle, Luke Published in Electronic notes in discrete mathematics (01.11.2015)“...Kostochka and Yancey proved that every 5critical graph G satisfies: E(G)≥94V(G)−54. A construction of Ore gives an infinite family of graphs meeting this...”

19by Hatami, Hamed Hladký, Jan Králʼ, Daniel Norine, Serguei Razborov, Alexander Published in Journal of combinatorial theory. Series A (01.04.2013)“...Using the formalism of flag algebras, we prove that every trianglefree graph G with n vertices contains at most (n/5)5 cycles of length five. Moreover, the...”

20“...The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum...”