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Almost-Rainbow Edge-Colorings of Some Small Subgraphs

100%

Krop E., Krop I.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

771-784

Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that [...] , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing [...] and for all even n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color the edges of G so that every C4 ⊆ G is colored by at least three colors. This improves the best known upper bound of Axenovich, Füredi, and Mubayi.

Distance Magic Cartesian Products of Graphs

81%

Cichacz S., Froncek D., Krop E., Raridan C.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

299-308

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant. In this paper, we show that hypercubes with dimension divisible by four are not distance magic. We also provide some positive results by proving necessary and sufficient conditions for the Cartesian product of certain complete multipartite graphs and the cycle on four vertices to be distance magic.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Krop E.

1 Cichacz S.

1 Froncek D.

1 Krop I.

1 Raridan C.

1 2016

1 2013

Wyniki wyszukiwania

Almost-Rainbow Edge-Colorings of Some Small Subgraphs

Distance Magic Cartesian Products of Graphs