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

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

Publications de l'Institut Mathématique. Nouvelle Série

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### Structural Properties of Recursively Partitionable Graphs with Connectivity 2

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...

### Conditional resolvability in graphs: a survey.

International Journal of Mathematics and Mathematical Sciences

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### Gradual partition of a graph into complete graphs

Časopis pro pěstování matematiky

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### A new class of enumeration problems

Czechoslovak Mathematical Journal

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### Degree Sequences of Monocore Graphs

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 − [...] .

### On graphs with prescribed subgraphs of order $k$, and a theorem of Kelly and Merriell

Czechoslovak Mathematical Journal

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### Non-complete extended $P$-sum of graphs, graph angles and star partitions.

Publications de l'Institut Mathématique. Nouvelle Série

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### Note on Strong Product of Graphs

Kragujevac Journal of Mathematics

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### Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected ${P}_{3}$-graphs.

The Electronic Journal of Combinatorics [electronic only]

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### Partitions of some planar graphs into two linear forests

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...