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 ...
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...
On decomposing regular graphs into locally irregular subgraphs We also support this conjecture by showing that decompositions into three or two such subgraphs might be indicated e.g. for some bipartite graphs (including trees), complete graphs and cartesian products of graphs with this property (.....
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//www.kdnuggets.com/datasets/index.html Hub https://github.com/activeloopai/Hub 40.Datasets for Machine Learning on Graphs-https://ogb.stanford.edu/ 41.https://www.johnsnowlabs.com/data/ 42.30 largest tensorflow datasets-https://lionbridge.ai/datasets/tensorflow-datasets-machine-learning/ 43...
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2 2 The (k, ℓ)-rainbow index for complete bipartite graphs This section is devoted to the (k, ℓ)-rainbow index for complete bipartite graphs. We start with a lemma about the regular complete bipartite graphs Kn,n. Lemma 2.1. For every pair of positive integers k, ℓ with k ≥...
#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...
P. Horn, Rainbow spanning trees in complete graphs colored by one-factorizations, J. Graph Theory 87 (2018), no. 3, 333-346.Paul Horn. Rainbow spanning trees in complete graphs colored by one factorizations. Preprint, 2013.P. Horn. Rainbow spanning trees in complete graphs colored by one-...
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 ...