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- W2894004003 abstract "A heterochromatic (or rainbow) graph is an edge-colored graph whose edges have distinct colors, that is, where each color appears at most once. In this paper, I propose a $(g,f)$-chromatic graph as an edge-colored graph where each color $c$ appears at least $g(c)$ times and at most $f(c)$ times. I also present a necessary and sufficient condition for edge-colored graphs (not necessary to be proper) to have a $(g,f)$-chromatic spanning tree. Using this criterion, I show that an edge-colored complete graph $G$ has a spanning tree with a color probability distribution `similar' to that of $G$. Moreover, I conjecture that an edge-colored complete graph $G$ of order $2n$ $(n ge 3)$ can be partitioned into $n$ edge-disjoint spanning trees such that each has a color probability distribution `similar' to that of $G$." @default.
- W2894004003 created "2018-10-05" @default.
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- W2894004003 date "2018-09-27" @default.
- W2894004003 modified "2023-10-18" @default.
- W2894004003 title "$(g,f)$-Chromatic spanning trees and forests" @default.
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- W2894004003 doi "https://doi.org/10.48550/arxiv.1809.10355" @default.
- W2894004003 hasPublicationYear "2018" @default.
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