ﻻ يوجد ملخص باللغة العربية
We give a necessary and sufficient condition for a $P_4$-free graph to be a cograph. This allows us to obtain a simple proof of the fact that finite $P_4$-free graphs are finite cographs. We also prove that chain complete posets whose comparability graph is a cograph are series-parallel.
Using a modified version of jeu de taquin, Novelli, Pak and Stoyanovskii gave a bijective proof of the hook-length formula for counting standard Young tableaux of fixed shape. In this paper we consider a natural extension of jeu de taquin to arbitrar
Motivated by generalizing Khovanovs categorification of the Jones polynomial, we study functors $F$ from thin posets $P$ to abelian categories $mathcal{A}$. Such functors $F$ produce cohomology theories $H^*(P,mathcal{A},F)$. We find that CW posets,
Arboricity is a graph parameter akin to chromatic number, in that it seeks to partition the vertices into the smallest number of sparse subgraphs. Where for the chromatic number we are partitioning the vertices into independent sets, for the arborici
We show that every countable cograph has either one or infinitely many siblings. This answers, very partially, a conjecture of Thomasse. The main tools are the notion of well quasi ordering and the correspondence between cographs and some labelled ordered trees.
We consider 3 (weighted) posets associated with a graph G - the poset P(G) of distinct induced unlabelled subgraphs, the lattice Omega(G) of distinct unlabelled graphs induced by connected partitions, and the poset Q(G) of distinct unlabelled edge-su