On the chromatic number of regular matroids
نویسندگان
چکیده
منابع مشابه
The Chromatic Number of Random Regular Graphs
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
متن کاملOn the b-chromatic number of regular graphs.dvi
The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular graph with girth g = 5 is at least ⌊ d+...
متن کاملOn the b-chromatic number of regular graphs
The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular graph with girth g = 5 is at least ⌊ d+...
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It was only recently shown by Shi and Wormald, using the differential equation method to analyse an appropriate algorithm, that a random 5-regular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5-regular graph is asymptotically almost surely equal to 3, provided a certain four-variable function has a unique maximum at a giv...
متن کاملOn the chromatic number of random regular graphs
In this work we show that, for any fixed d, random d-regular graphs asymptotically almost surely can be coloured with k colours, where k is the smallest integer satisfying d < 2(k−1) log(k−1). From previous lower bounds due to Molloy and Reed, this establishes the chromatic number to be asymptotically almost surely k − 1 or k. If moreover d > (2k−3) log(k−1), then the value k−1 is discarded and...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1978
ISSN: 0095-8956
DOI: 10.1016/0095-8956(78)90057-6