Geodesic
Degree sequences of monocore graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 585-592

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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 d_1, . . ., d_n 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 ⨊d_i = 2m, where m satisfies ⌈k·n/2⌉ ≤ m ≤ k ・ n − k+12
Keywords: monocore graph, degeneracy, degree sequence 
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Bickle, Allan. Degree sequences of monocore graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 585-592. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a10/