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ESA
2008
Springer
127views Algorithms» more  ESA 2008»
15 years 1 months ago
The Alcuin Number of a Graph
We consider a planning problem that generalizes Alcuin's river crossing problem (also known as: The wolf, goat, and cabbage puzzle) to scenarios with arbitrary conflict graph...
Péter Csorba, Cor A. J. Hurkens, Gerhard J....
EJC
2008
14 years 12 months ago
Fractional chromatic number of distance graphs generated by two-interval sets
Let D be a set of positive integers. The distance graph generated by D, denoted by G(Z, D), has the set Z of all integers as the vertex Supported in part by the National Science ...
Daphne Der-Fen Liu, Xuding Zhu
ENDM
2002
134views more  ENDM 2002»
14 years 11 months ago
Bounds on the signed domination number of a graph
Let G = (V, E) be a simple graph on vertex set V and define a function f : V {-1, 1}. The function f is a signed dominating function if for every vertex x V, the closed neighbor...
Ruth Haas, Thomas B. Wexler
WG
2010
Springer
14 years 10 months ago
The Number of Bits Needed to Represent a Unit Disk Graph
We prove that for sufficiently large n, there exist unit disk graphs on n vertices such that for every representation with disks in the plane at least c √ n bits are needed to wr...
Colin McDiarmid, Tobias Müller
JGT
2007
85views more  JGT 2007»
14 years 11 months ago
On graphs with subgraphs having large independence numbers
: Let G be a graph on n vertices in which every induced subgraph on s = log3 n vertices has an independent set of size at least t = log n. What is the largest q = q(n) so that ever...
Noga Alon, Benny Sudakov