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.
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
.
DOI: 10.1007/s40305-022-00409-5
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