We also show that if the lower bound on minimum degree is replaced by a constant (however large it may be), then neither a 2o(n) time nor a 2o(m) time algorithm is possible (m denotes the number of edges) for 3-colorability unless Exponential Time Hypothesis (ETH) fails.
Since for any subgraph consisting of v, its minimum degree is no greater than deg v).
By Theorem 12, a node v cannot be included in any subgraph whose minimum degree is larger than (c_v).
Compared with k-core model, whose lower bound of minimum degree is a constant k, the minimum degree of a k-plex is increased with its cardinality.
Let (delta (H) > c_v) and (H) denote (delta (H -core) of G, tH -coresubset H), ofherwise, (H cup H) would result in a larGer subgraph whose minimum degree is no less then (delta (H)), contradicting (H) isubsetmized.
The mean degree is between d and 2 d, the minimum degree is d, and the maximum degree can be as large as n - 1, with n being the number of genes in the network.
The model so defined was chosen with basis functions defined over a cap with a semi-angle of 16°, in order to represent the main field and its secular variation, including the most significant harmonics of the regional geomagnetic field (the minimum and maximum degrees are approximately equal to 6.1 and 13.2, respectively).
This index (i.e. C D ) attains its minimum value of 0 when all degrees are equal (i.e. the situation in a circle graph).
Since the quantity 2lnN never exceeds 10, our maximum threshold condition (minimum mean degree) was determined by the requirement for obtaining fully connected graphs.
However, the minimum node degree was not given.
