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The packing chromatic number χ ρ ( G ) of a graph G is the smallest integer k such that there exists a k -vertex coloring of G in which any two vertices receiving color i are at distance at least i + 1 . It is proved that in the class of subcubic graphs the packing chromatic number is bigger than 13 , thus answering an open problem from Gastineau and Togni (2016). In addition,...
Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for two classes of cubic graphs, cubic graphs with a circuit missing only one vertex and bridgeless cubic graphs having a 2-factor with exactly two circuits. The first part of this result implies that Berge Conjecture...
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