ABSTRACT Summary: "We consider the coloring of edges in a graph in which there are verti... more ABSTRACT Summary: "We consider the coloring of edges in a graph in which there are vertices of three types. In a feasible edge coloring, each vertex of the first type is incident with at least two edges of the same color, and each vertex of the second type with at least two edges of different colors, while no constraints are required for the vertices of the third type. We present a characterization of colorable graphs and a linear-time algorithm to decide whether a given graph with prescribed vertex types admits a feasible edge coloring.''
Every partially ordered set P on at least (1+o(1))n3 elements can be decomposed into subposets of... more Every partially ordered set P on at least (1+o(1))n3 elements can be decomposed into subposets of size n that are ‘almost’ chains or antichains. This lower bound on P is asymptotically best possible. Similar results are presented for other types of combinatorial structures.
We investigate the largest number of colours, called upper chromatic number and denoted X(H), tha... more We investigate the largest number of colours, called upper chromatic number and denoted X(H), that can be assigned to the vertices (points) of a Steiner triple system H in such a way that every block H ∈ H contains at least two vertices of the same colour. The exact value of X is determined for some classes of triple systems,
ABSTRACT Summary: "We consider the coloring of edges in a graph in which there are verti... more ABSTRACT Summary: "We consider the coloring of edges in a graph in which there are vertices of three types. In a feasible edge coloring, each vertex of the first type is incident with at least two edges of the same color, and each vertex of the second type with at least two edges of different colors, while no constraints are required for the vertices of the third type. We present a characterization of colorable graphs and a linear-time algorithm to decide whether a given graph with prescribed vertex types admits a feasible edge coloring.''
Every partially ordered set P on at least (1+o(1))n3 elements can be decomposed into subposets of... more Every partially ordered set P on at least (1+o(1))n3 elements can be decomposed into subposets of size n that are ‘almost’ chains or antichains. This lower bound on P is asymptotically best possible. Similar results are presented for other types of combinatorial structures.
We investigate the largest number of colours, called upper chromatic number and denoted X(H), tha... more We investigate the largest number of colours, called upper chromatic number and denoted X(H), that can be assigned to the vertices (points) of a Steiner triple system H in such a way that every block H ∈ H contains at least two vertices of the same colour. The exact value of X is determined for some classes of triple systems,
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Papers by Zsolt Tuza