Chvátal–Erdős Conditions and Almost Spanning Trails

Autor: Lan Lei, Mingquan Zhan, Xiaomin Li, Hong-Jian Lai, Xiaoling Ma
Rok vydání: 2020
Předmět:
Zdroj: Bulletin of the Malaysian Mathematical Sciences Society. 43:4375-4391
ISSN: 2180-4206
0126-6705
DOI: 10.1007/s40840-020-00928-5
Popis: Let $$\alpha '(G), ess'(G), \kappa (G), \kappa '(G), N_G(v)$$ and $$D_i(G)$$ denote the matching number, essential edge connectivity, connectivity, edge connectivity, the set of neighbors of v in G and the set of degree i vertices of a graph G, respectively. For $$u, v\in V(G)$$ , define $$u\sim v$$ if and only if $$u=v$$ or both $$u, v\in D_{2}(G)$$ and $$N_{G}(u)=N_{G}(v)$$ . Then, $$\sim $$ is an equivalence relation, and [v] denotes the equivalence class containing v. A subgraph H of G is almost spanning if $$H\subseteq G-D_{1}(G), \bigcup _{j \ge 3} D_{j}(G) \subseteq V(H)$$ and for any $$v\in D_2(G), |[v]-V(H)|\le 1$$ . The line graph version of Chvatal–Erdős theorem for a connected graph G are extended as follows.
Databáze: OpenAIRE
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