On the (k, i)-coloring of cacti and complete graphs
In the (k, i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph C, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k, i)-chro...
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| Autores principales: | , , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03817032_v137_n_p317_Bonomo |
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| Sumario: | In the (k, i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph C, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k, i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (k, i)- coloring of cycles and we generalize the result in order to derive a polynomial time algorithm for this problem on cacti. We also perform a slight modification to the algorithm in order to obtain a simpler algorithm for the close coloring problem addressed in [R.C. Brigham and R.D. Dutton, Generalized fc-tuple colorings of cycles and other graphs, J. Combin. Theory B 32:90-94, 1982], Finally, we present a relation between the (k,i)-coloring problem on complete graphs and weighted binary codes. © 2018 Charles Babbage Research Centre. All rights reserved. |
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