37,320 research outputs found
A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market
We present the first combinatorial polynomial time algorithm for computing
the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201
Thomassen's Choosability Argument Revisited
Thomassen (1994) proved that every planar graph is 5-choosable. This result
was generalised by {\v{S}}krekovski (1998) and He et al. (2008), who proved
that every -minor-free graph is 5-choosable. Both proofs rely on the
characterisation of -minor-free graphs due to Wagner (1937). This paper
proves the same result without using Wagner's structure theorem or even planar
embeddings. Given that there is no structure theorem for graphs with no
-minor, we argue that this proof suggests a possible approach for
attacking the Hadwiger Conjecture
Conservative constraint satisfaction re-revisited
Conservative constraint satisfaction problems (CSPs) constitute an important
particular case of the general CSP, in which the allowed values of each
variable can be restricted in an arbitrary way. Problems of this type are well
studied for graph homomorphisms. A dichotomy theorem characterizing
conservative CSPs solvable in polynomial time and proving that the remaining
ones are NP-complete was proved by Bulatov in 2003. Its proof, however, is
quite long and technical. A shorter proof of this result based on the absorbing
subuniverses technique was suggested by Barto in 2011. In this paper we give a
short elementary prove of the dichotomy theorem for the conservative CSP
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