On the chromatic index of outerplanar graphs
نویسندگان
چکیده
منابع مشابه
Algorithms for the Strong Chromatic Index of Halin Graphs, Distance-Hereditary Graphs and Maximal Outerplanar Graphs
We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.
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The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the weak ...
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Let χ(G) denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1y3, y3y5, y5y1 to a 6-cycle y1y2 · · · y6y1. In this paper, it is proved that ∆+1 ≤ χ(G ) ≤ ∆+2, and χ(G) = ∆ + 2 if and only if G is Q, where ∆ represents the maximum degree of G.
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The strong chromatic index of a graph G, denoted by χs(G), is the minimum number of colors needed to color its edges so that each color class is an induced matching. In this paper we analyze the asymptotic behavior of this parameter in a random graph G(n, p), for two regions of the edge probability p = p(n). For the dense case, where p is a constant, 0 < p < 1, we prove that with high probabili...
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We consider two graph colouring problems in which edges at distance at most t are given distinct colours, for some fixed positive integer t. We obtain two upper bounds for the distance-t chromatic index, the least number of colours necessary for such a colouring. One is a bound of (2− ε)∆t for graphs of maximum degree at most ∆, where ε is some absolute positive constant independent of t. The o...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1975
ISSN: 0095-8956
DOI: 10.1016/0095-8956(75)90060-x