A k-monocore graph is a graph which has its minimum degree and degeneracy both equal to k. Integer sequences that can be the degree sequence of some k-monocore graph are characterized as follows. A nonincreasing sequence of integers d0, . . . , dn is the degree sequence of some k-monocore graph G, 0 ≤ k ≤ n − 1, if and only if k ≤ di ≤ min {n − 1, k + n − i} and ⨊di = 2m, where m satisfies [...] ≤ m ≤ k ・ n − [...] .
@article{bwmeta1.element.doi-10_7151_dmgt_1759,
author = {Allan Bickle},
title = {Degree Sequences of Monocore Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {585-592},
zbl = {1295.05192},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1759}
}
Allan Bickle. Degree Sequences of Monocore Graphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 585-592. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1759/
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