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Papers by Anton Kundrík
Elsevier eBooks, 1992
Publisher Summary This chapter describes the harmonious chromatic number of a graph. A k-coloring... more Publisher Summary This chapter describes the harmonious chromatic number of a graph. A k-coloring of the graph G is a mapping of V(G) onto the set {1, 2,. . . , k}. The color of the edge e = uw is f(e) = (f(u), f(v)}. A harmonious k-coloring is defined as a k-coloring with adjacent vertices receiving different colors and all edges receiving different color pairs. The harmonious chromatic number of a graph G is the minimum k for which G has a harmonious k-coloring. The number h(G) has been determined for paths and cycles. Lee and Mitchem have found an upper bound for h(G) where G is an arbitrary graph. Mitchem has found an upper bound for the harmonious chromatic number of the complete binary tree. Some theorems and their proofs are also given in the chapter.
Mathematica Slovaca, 1990
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz
Dual point-partition number of a graph G with respect to a hereditary property P is the maximum n... more Dual point-partition number of a graph G with respect to a hereditary property P is the maximum number of disjoint point-induced subgraphs contained in G such that any subgraph does not have the property P. In this article, problems of the Nordhaus-Gaddum type for the dual point-partition number are investigated.
Annals of Discrete Mathematics, 1992
Annals of Discrete Mathematics, 1992
Elsevier eBooks, 1992
Publisher Summary This chapter describes the harmonious chromatic number of a graph. A k-coloring... more Publisher Summary This chapter describes the harmonious chromatic number of a graph. A k-coloring of the graph G is a mapping of V(G) onto the set {1, 2,. . . , k}. The color of the edge e = uw is f(e) = (f(u), f(v)}. A harmonious k-coloring is defined as a k-coloring with adjacent vertices receiving different colors and all edges receiving different color pairs. The harmonious chromatic number of a graph G is the minimum k for which G has a harmonious k-coloring. The number h(G) has been determined for paths and cycles. Lee and Mitchem have found an upper bound for h(G) where G is an arbitrary graph. Mitchem has found an upper bound for the harmonious chromatic number of the complete binary tree. Some theorems and their proofs are also given in the chapter.
Mathematica Slovaca, 1990
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz
Dual point-partition number of a graph G with respect to a hereditary property P is the maximum n... more Dual point-partition number of a graph G with respect to a hereditary property P is the maximum number of disjoint point-induced subgraphs contained in G such that any subgraph does not have the property P. In this article, problems of the Nordhaus-Gaddum type for the dual point-partition number are investigated.
Annals of Discrete Mathematics, 1992
Annals of Discrete Mathematics, 1992