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Research on fractional critical covered graphs. (English. Russian original) Zbl 1458.05221
Probl. Inf. Transm. 56, No. 3, 270-277 (2020); translation from Probl. Peredachi Inf. 56, No. 5, 77-85 (2020).
Summary: A graph $$G$$ is called a fractional $$(g, f)$$-covered graph if for any $$e \in E(G), G$$ admits a fractional $$(g, f)$$-factor covering $$e$$. A graph $$G$$ is called a fractional $$(g, f, n)$$-critical covered graph if for any $$S \subseteq V(G)$$ with $$\vert S \vert = n$$, $$G - S$$ is a fractional $$(g, f)$$-covered graph. A fractional $$(g, f, n)$$-critical covered graph is said to be a fractional $$(a, b, n)$$-critical covered graph if $$g(x) = a$$ and $$f(x) = b$$ for every $$x \in V(G)$$. A fractional $$(a, b, n)$$-critical covered graph was first defined and studied in [S. Zhou et al., Inf. Process. Lett. 152, Article ID 105838, 5 p. (2019; Zbl 07115185)]. In this article, we investigate fractional $$(g, f, n)$$-critical covered graphs and present a binding number condition for the existence of fractional $$(g, f, n)$$-critical covered graphs, which is an improvement and generalization of a previous result obtained in [Y. Yuan and R.-X. Hao, Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 157–167 (2020; Zbl 1433.05264)].

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C72 Fractional graph theory, fuzzy graph theory
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