An independent set of three vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third. A graph is asteroidal triplefree (AT-free) if it contains no asteroidal triple. The motivation for this investigation is provided, in part, by the fact that AT-free graphs offer a common generalization of interval, permutation, tra...

let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...

We show that the square of every connected S(K1,4)-free graph satisfying a matching condition has 2-connected spanning subgraph maximum degree at most 3. Furthermore, we characterise trees whose k. This generalises results on S(K1,3)-free graphs Henry and Vogler [7] Harary Schwenk [6], respectively.

We prove that every 3-chromatic claw-free perfect graph is 3-choosable. c © 2003 Elsevier B.V. All rights reserved.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 16 December 2019Accepted: 05 May 2021Published online: 02 September 2021Keywordsconflict-free coloring, kernelization, fixed-parameter tractability, combinatorial boundsAMS Subject Headings68Q25, 05C15Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publishe...