Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 30 November 2020Accepted: 26 July 2021Published online: 18 2021Keywordscounting modulo 2, counting complexity, graph homomorphisms, parity complexity dichotomyAMS Subject Headings68Q17, 68Q25Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society...

A vertex of a graph is bisimplicial if the set its neighbors union two cliques; quasi-line every bisimplicial. recent result Chudnovsky and Seymour asserts that non-empty even-hole-free has vertex. Both Hadwiger's conjecture Erdős-Lovász Tihany have been shown to be true for graphs, but are open graphs. In this note, we prove $G$ with $\omega(G)<\chi(G)=s+t-1$ satisfies provided $ t\geq s &g...

The codegree threshold ex 2 ( n , F ) $\operatorname{ex}_2(n, F)$ of a 3-graph $F$ is the minimum d = $d=d(n)$ such that every on $n$ vertices in which pair contained at least + 1 $d+1$ edges contains copy as subgraph. We study when K 4 − $F=K_4^-$ with 3 edges. Using flag algebra techniques, we prove if sufficiently large, then ⩽ . $$\begin{equation*} \hspace*{76pt}\operatorname{ex}_2(n, K_4^-...

We introduce the class of outerspatial 2-complexes as natural generalisation outerplanar graphs to three dimensions. Answering a question O-joung Kwon, we prove that locally 2-connected 2-complex is if and only it does not contain surface positive genus subcomplex have space minor generalised cone over $K_4$ or $K_{2,3}$.
 This applied nested plane embeddings graphs; is, constrained by con...

In this paper, it is proved that all simple $K_4$-groups of type $L_2(q)$ can be characterized by their maximum element orders together with their orders. Furthermore, the automorphism groups of simple $K_4$-groups of type $L_2(q)$ are also considered.

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...