Displaying similar documents to “On degree sequences of graphs with given cyclomatic number.”

Structural Properties of Recursively Partitionable Graphs with Connectivity 2

Olivier Baudon, Julien Bensmail, Florent Foucaud, Monika Pilśniak (2017)

Discussiones Mathematicae Graph Theory

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A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1, . . . , np) of |V (G)| there exists a partition (V1, . . . , Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition...

Degree Sequences of Monocore Graphs

Allan Bickle (2014)

Discussiones Mathematicae Graph Theory

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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 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 − [...] .