منابع مشابه
On the Strong Parity Chromatic Number
A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of pla...
متن کاملOn the Strong Chromatic Number of Graphs
The strong chromatic number, χS(G), of an n-vertex graph G is the smallest number k such that after adding kdn/ke−n isolated vertices to G and considering any partition of the vertices of the resulting graph into disjoint subsets V1, . . . , Vdn/ke of size k each, one can find a proper k-vertex-coloring of the graph such that each part Vi, i = 1, . . . , dn/ke, contains exactly one vertex of ea...
متن کاملxx ( xxxx ) 1 – 14 2 ON THE STRONG PARITY CHROMATIC NUMBER
12 A vertex colouring of a 2-connected plane graph G is a strong parity 13 vertex colouring if for every face f and each colour c, the number of 14 vertices incident with f coloured by c is either zero or odd. 15 Czap et al. in [9] proved that every 2-connected plane graph has a 16 proper strong parity vertex colouring with at most 118 colours. 17 In this paper we improve this upper bound for s...
متن کاملOn the Strong Chromatic Number of Random Graphs
Let G be a graph with n vertices, and let k be an integer dividing n. G is said to be strongly k-colorable if for every partition of V (G) into disjoint sets V1 ∪ . . . ∪ Vr, all of size exactly k, there exists a proper vertex k-coloring of G with each color appearing exactly once in each Vi. In the case when k does not divide n, G is defined to be strongly k-colorable if the graph obtained by ...
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2011
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1567