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Dense Arbitrarily Partitionable Graphs

100%

Kalinowski R., Pilśniak M., Schiermeyer I., Woźniak M.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 1

5-22

A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . . , Vk) of the vertex set V (G) such that Vi induces a connected subgraph of order ni for i = 1, . . . , k. In this paper we show that every connected graph G of order n ≥ 22 and with [...] ‖G‖ > (n−42)+12 $||G||\; > \;\left( {\matrix{{n - 4} \cr 2 \cr } } \right) + 12$ edges is AP or belongs to few classes of exceptional graphs.

Distinguishing Cartesian Products of Countable Graphs

88%

Estaji E., Imrich W., Kalinowski R., Pilśniak M., Tucker T.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

155-164

The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Kalinowski R.

2 Pilśniak M.

1 Estaji E.

1 Imrich W.

1 Schiermeyer I.

1 Tucker T.

1 Woźniak M.

1 2017

1 2016

Wyniki wyszukiwania

Dense Arbitrarily Partitionable Graphs

Distinguishing Cartesian Products of Countable Graphs