✍ Scribed by Chen Shaozhu; Huang Qingguang
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📜 SIMILAR VOLUMES
This article is motivated by a conjecture of Thomassen and Toft on the number s 2 (G) of separating vertex sets of cardinality 2 and the number v 2 (G) of vertices of degree 2 in a graph G belonging to the class G of all 2-connected graphs without nonseparating induced cycles. Let G denote the numbe
## Abstract Wang and Williams defined a __threshold assignment__ for a graph __G__ as an assignment of a non‐negative weight to each vertex and edge of __G__, and a threshold __t__, such that a set __S__ of vertices is stable if and only if the total weight of the subgraph induced by __S__ does not
## Abstract It is shown that, for all sufficiently large __k__, the complete graph __K~n~__ can be decomposed into __k__ factors of diameter 2 if and only if __n__ ≥ 6__k__.
We prove that if \(\lambda\) is an infinite cardinal number and \(G\) is any graph of cardinality \(\kappa=\lambda^{+}\)which is a union of a finite number of forests, then there is a graph \(H_{k}\) of size \(\kappa\) (which does not depend upon \(G\) ) so that \(H_{k} \rightarrow(G)_{k}^{1}\). Röd