The main emphasis of this paper is a classification of those forbidden rainbow graphs that force a low number of vertices of a high color degree, along with some specifications and more general information in certain cases. Those graphs turn out to be of two special types of trees of small ...
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Finally, we investigate the notion of λ-complete colourings of graphs (i.e., 2-uniform hypergraphs). We show that λ-complete colourings have the same interpolation property as complete colourings. Moreover, we prove that it is NP-complete to decide whether a tree with c2 edges has a ...
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(Herscovici [6])For any connected graphsand, Gao and Yin [4] proved that ifis a tree, or a complete graph, or an even cycle andhas the-pebbling property, then Conjecture 1.2 holds. Kirlangic [7] defined a thorn graph of the graphas follows: Letbe a graph withandbe positive intege...
Gallai-colorings of complete graphs–edge colorings such that no triangle is colored with three distinct colors–occur in various contexts such as the theory of partially ordered sets (in Gallai’s original paper), information theory and the theory of perfect graphs. We extend here Gallai-colorin...
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#1042. Flower Planting With No Adjacent(E+) 1300 #1153. String Transform into another String (H-) 1700 #1192. Critical Connection (H) 1900 #1245. Tree Diameter (M-) 1400 #1334. Find the City With the Smallest Number of Neighbors at a Threshold Distance (M) 1500 (Floyd-Warshall...
Rainbow spanning tree decompositions in complete graphs colored by cyclic 1-factorizations1-factorizationsRainbow spanning treesComplete graphBrualdi and Hollingsworth conjectured in Brualdi and Hollingsworth (1996) that in any complete graph K-2n, n >= 3, which is properly colored with 2n - 1 ...
We consider the 3-rainbow index of complete bipartite graphs K_(s,t). For 3 ≤ s ≤ t, we have determined the tight bounds of rx_3(K_(s,t))- In this paper, we continue the study. For 2 = s ≤ t, we develop a converse idea and apply with the model of chessboard to study...