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

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...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) 2024-06, Vol.12 (2), p.446-460
Main Authors: Gao, Wei, Wang, Wei-Fan
Format: Article
Language:English
Subjects:
Data transmission
Graphs
Management Science
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research
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Summary: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.
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-022-00409-5