Total chromatic number of regular graphs of odd order and high degree
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چکیده
منابع مشابه
The total chromatic number of regular graphs of even order and high degree
The total chromatic number T (G) of a graph G is the minimum number of colours needed to colour the edges and the vertices ofG so that incident or adjacent elements have distinct colours. We show that if G is a regular graph of even order and (G) 3 |V (G)| + 23 6 , then T (G) (G)+ 2. © 2005 Elsevier B.V. All rights reserved.
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If G is a simple graph with minimum degree <5(G) satisfying <5(G) ^ f(| K(C?)| -f-1) the total chromatic number conjecture holds; moreover if S(G) ^ f| V(G)\ then #T(G) < A(G) + 3. Also if G has odd order and is regular with d{G) ^ \^/1\V{G)\ then a necessary and sufficient condition for ^T((7) = A((7)+ 1 is given.
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A Steinhaus matrix is a binary square matrix of size n which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy ai,j = ai−1,j−1+ai−1,j for all 2 6 i < j 6 n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states...
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Let G be a graph of order 2n+ 1 having maximum degree 2n—\. We prove that the total chromatic number of G is 2/i if and only if e(G — w) + oc'(G — w)^n, where w is a vertex of minimum degree in G, G — w is the complement of G — w, e(G — w) is the size of G — w, and a'(G-w) is the edge independence number of G — w.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00034-t