منابع مشابه
L(h, 1, 1)-Labeling of Outerplanar Graphs
An L(h, 1, 1)-labeling of a graph is an assignment of labels from the set of integers {0, · · · , λ} to the vertices of the graph such that adjacent vertices are assigned integers of at least distance h ≥ 1 apart and all vertices of distance three or less must be assigned different labels. The aim of the L(h, 1, 1)-labeling problem is to minimize λ, denoted by λh,1,1 and called span of the L(h,...
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An L(2, 1)-labeling of a graph G is an assignment of a nonnegative integer to each vertex of G such that adjacent vertices receive integers that differ by at least two and vertices at distance two receive distinct integers. The span of such a labeling is the difference between the largest and smallest integers used. The λ-number of G, denoted by λ(G), is the minimum span over all L(2, 1)-labeli...
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We show that the shortest-path metric of any k-outerplanar graph, for any fixed k, can be approximated by a probability distribution over tree metrics with constant distortion and hence also embedded into 1 with constant distortion. These graphs play a central role in polynomial time approximation schemes for many NP-hard optimization problems on general planar graphs and include the family of ...
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A (2, 1)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set {0, 1, . . . , k} of nonnegative integers such that | f (x) − f (y)| ≥ 2 if x is a vertex and y is an edge incident to x, and | f (x) − f (y)| ≥ 1 if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). The (2, 1)-total labeling number...
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A graph is called fractional ( r s , d ) -defective colorable if its vertices can be colored with r colors in such a way that each vertex receives s distinct colors and has at most d defects (a defect corresponds to the situation when two adjacent vertices are assigned with non-disjoint sets). We show that each outerplanar graph having no triangle faces sharing a vertex is fractional ( 7 3 , 1 ...
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ژورنال
عنوان ژورنال: Mathematical Methods of Operations Research
سال: 2008
ISSN: 1432-2994,1432-5217
DOI: 10.1007/s00186-008-0261-6