On Fractional (g, f, n’, m)-Critical Covered Graphs

doi:10.1007/s40305-022-00409-5

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (2): 446-460.doi: 10.1007/s40305-022-00409-5

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On Fractional (g, f, n’, m)-Critical Covered Graphs

Wei Gao¹, Wei-Fan Wang²

1 School of Information Science and Technology, Yunnan Normal University, Kunming 650500, Yunnan, China;
2 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

Received:2021-09-06 Revised:2022-02-18 Online:2024-06-30 Published:2024-06-12
Contact: Wei Gao, Wei-Fan Wang E-mail:gaowei@ynnu.edu.cn;wwf@zjnu.cn
Supported by:
The research is partially supported by the National Natural Science Foundation of China (Nos. 12161094 and 12031018).

Abstract

Abstract: The main contribution in this article is threefold: (1) we show the necessary and sufficient condition for graphs to be fractional (g, f)-covered which can be expressed in different forms, and extended to fractional (g, f, m)-covered graphs; (2) the concept of fractional (g, f, n’, m)-critical covered graph is put forward and its necessary and sufficient condition is given; (3) we present the degree condition for a graph to be fractional (g, f, n’, m)-critical covered, and show that degree bound is sharp when m is small. Moreover, the related result in fractional (a, b, n’, m)-critical covered setting is also verified.

Key words: Network, Fractional factor, Data transmission, Fractional covered graph, Fractional critical covered graph

CLC Number:

05C70

Wei Gao, Wei-Fan Wang. On Fractional (g, f, n’, m)-Critical Covered Graphs[J]. Journal of the Operations Research Society of China, 2024, 12(2): 446-460.

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References

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On Fractional (g, f, n’, m)-Critical Covered Graphs

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