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推崇

A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphswhen restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(.), and construct a tree with at least (. − x(.) + 4)/3 leaves, and prove that no tree with more than (. − x(.) + 2)/2 leaves exists. In contrast to

epinephrine

On the Pseudo-achromatic Number Problem be partitioned into . groups such that every two groups are connected by at least one edge. This problem has been extensively studied in graph theory and combinatorial optimization. We show that the problem has a kernel of at most (. − 2)(. + 1) vertices that is constructable in time ., where . and

GLUE

Making Role Assignment Feasible: A Polynomial-Time Algorithm for Computing Ecological Colorings of the graph, such that two nodes surrounded by the same set of roles must be assigned the same role (Borgatti and Everett, 1992). We prove that, for any simple undirected graph . with . distinct neighborhoods and for any integer . with 1 ≤ . ≤ ., . admits an ecological coloring which uses exactly

喷出

Faster Exact Bandwidthn. In 2000, Feige an Kilian [4] came up with a ..(10.)-time algorithm. Since then there has been a growing interest in exponential time algorithms but this bound has not been improved..In this paper we present a new and quite simple ..(5.) algorithm. We also obtain even better bound in some special

AMBI

Additive Spanners for Circle Graphs and Polygonal Graphshat for any two vertices .,. of . a spanning tree .(.) exists such that the distance in . between . and . is at most . plus their distance in .. In this paper, we examine the problem of finding “small” systems of collective additive tree .-spanners for small values of . on circle graphs and on polyg

江湖骗子

Mundane

Complexity of the Packing Coloring Problem for Trees.. We solve an open problem of Goddard et al. and show that the decision whether a tree allows a packing coloring with at most . classes is .-complete..We accompany this .-hardness result by a polynomial time algorithm for trees for closely related variant of the packing coloring problem where the l

宿醉

Characterizations of Restricted Pairs of Planar Graphs Allowing Simultaneous Embedding with Fixed Edh. . are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (.) has been open..We give a necessary and sufficient condition for whether a . exists for pairs of

使熄灭

Gentry

Evaluations of Graph Polynomialsas evaluations at specific points .. In this paper we study the question how to prove that a given graph parameter, say .(.), the size of the maximal clique of ., cannot be a fixed coefficient or the evaluation at any point of the Tutte polynomial, the interlace polynomial, or any graph polynomial o