## Displaying similar documents to “Evolutionary families of sets.”

### Decomposing infinite 2-connected graphs into 3-connected components.

The Electronic Journal of Combinatorics [electronic only]

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### The Balanced Decomposition Number of TK4 and Series-Parallel Graphs

Discussiones Mathematicae Graph Theory

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A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪˙ · · · ∪˙ Vr such that, for every i, Vi induces a connected subgraph of order at most s, and contains the same number of red and blue vertices. The...

### Even bonds of prescribed directed parity.

The Electronic Journal of Combinatorics [electronic only]

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### Disjoint triangles and quadrilaterals in a graph

Open Mathematics

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Let n, s and t be three integers with s ≥ 1, t ≥ 0 and n = 3s + 4t. Let G be a graph of order n such that the minimum degree of G is at least (n + s)/2. Then G contains a 2-factor with s + t components such that s of them are triangles and t of them are quadrilaterals.

### Connectivity of the lifts of a greedoid.

The Electronic Journal of Combinatorics [electronic only]

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### Heavy subgraph pairs for traceability of block-chains

Discussiones Mathematicae Graph Theory

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A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two...

### Parity versions of 2-connectedness.

The Electronic Journal of Combinatorics [electronic only]

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### Connectivity of path graphs.

Acta Mathematica Universitatis Comenianae. New Series

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### A degree condition for the existence of $k$-factors with prescribed properties.

International Journal of Mathematics and Mathematical Sciences

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### Vector spaces and the Petersen graph.

The Electronic Journal of Combinatorics [electronic only]

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### On eulerian irregularity in graphs

Discussiones Mathematicae Graph Theory

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A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G is an Eulerian walk that encounters no two edges of G the same number of times. The minimum...

### A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution

Compositio Mathematica

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