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JCT
2006
72views more  JCT 2006»
14 years 11 months ago
Arboricity and tree-packing in locally finite graphs
Nash-Williams' arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of vertices induces more than k( - 1) edges. We prove a...
Maya Jakobine Stein
LATIN
2010
Springer
15 years 4 months ago
Euclidean Prize-Collecting Steiner Forest
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euc...
MohammadHossein Bateni, MohammadTaghi Hajiaghayi
WG
2010
Springer
14 years 10 months ago
Colouring Vertices of Triangle-Free Graphs
The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it remains NP-complete even if we additionally exclude a graph F which is n...
Konrad Dabrowski, Vadim V. Lozin, Rajiv Raman, Ber...
ARSCOM
2002
70views more  ARSCOM 2002»
14 years 11 months ago
On the Number of Graphical Forest Partitions
A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. ...
Deborah A. Frank, Carla D. Savage, James A. Seller...
JGT
2010
127views more  JGT 2010»
14 years 10 months ago
On the minimum degree of minimal Ramsey graphs
We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr, Erd˝os, and Lov´asz. We determine the corresponding graph parameter fo...
Tibor Szabó, Philipp Zumstein, Stefanie Z&u...