### Vertex degree sequences of graphs with small number of circuits.

Gutman, Ivan (1989)

Publications de l'Institut Mathématique. Nouvelle Série

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Gutman, Ivan (1989)

Publications de l'Institut Mathématique. Nouvelle Série

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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...

Saenpholphat, Varaporn, Zhang, Ping (2004)

International Journal of Mathematics and Mathematical Sciences

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Josef Voldřich (1978)

Časopis pro pěstování matematiky

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Robert H. Johnson (1974)

Czechoslovak Mathematical Journal

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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 − [...] .

Yair Caro (1994)

Czechoslovak Mathematical Journal

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Cvetković, Dragoš, Simić, Slobodan (1993)

Publications de l'Institut Mathématique. Nouvelle Série

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M. Tavakoli, F. Rahbarnia, A. R. Ashrafi (2013)

Kragujevac Journal of Mathematics

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Li, Xueliang, Liu, Yan (2008)

The Electronic Journal of Combinatorics [electronic only]

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Piotr Borowiecki, Mariusz Hałuszczak (1997)

Discussiones Mathematicae Graph Theory

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A linear forest is a forest in which every component is a path. It is known that the set of vertices V(G) of any outerplanar graph G can be partitioned into two disjoint subsets V₁,V₂ such that induced subgraphs ⟨V₁⟩ and ⟨V₂⟩ are linear forests (we say G has an (LF, LF)-partition). In this paper, we present an extension of the above result to the class of planar graphs with a given number of internal vertices (i.e., vertices that do not belong to the external face at a certain fixed...