Proof We first give the proof for declining games. Consider the reachability game on the expansion with vertices V\times \mathbb {N} such that the target set is F\times \mathbb {N}. For k\in \mathbb {N} let W_k\subseteq V be the set of those vertices u such that Player 1 has ...
Parity Games of Bounded Tree- and Clique-Width 393 Proof. Consider the reward order on N, which intuitively sorts the priorities according to their attractivity to Player 0: We define p q if p and q are even and p ≤ q, or p and q are odd and p ≥ q, or p is odd and q is...
J. Czap, S. Jendroľ, M. Voigt, Parity vertex colouring of plane graphs, Discrete Math. 311 (6) (2011) 512-520.Parity vertex colouring of plane graphs - Czap, Jendrol’, et al. - 2011 () Citation Context ...oloring with at most 97 colors. The proof is given in Section 2....
Hence, our work provides the first proof that it is possible to manipulate and tailor MWP systems by exploiting non-Hermitian degeneracy phase transitions, paving the way for a new class of PT-symmetric MWP applications in the generation, processing, control and distribution of microwave and ...
ProofFor an MET-LDPC code ensemble of three edge types of\({{{\mathcal{E}}}_{1}=\{1\}\),\({{{\mathcal{E}}}_{2}=\{2\}\), and\({{{\mathcal{E}}}_{12}^{c}=\{3\}\)withgi,2 = 0 for all\(i\in {C}_{1}^{c}\), the ensemble in Eq. (1) can be rew...
Proof Choose n:=⌈k2⌉+k−1. The vertex d⌈k2⌉ is the first of the vertices d1,…,dn to be connected to the vertices A:={aj:j⩽k}. The k−1 vertices di, i=⌈k2⌉+1,…,⌈k2⌉+k−1 are connected to each vertex of A as well. Neither the vertices of ...
Discrete MathematicsCharles H.C. Little, The parity of the number of 1-factors of a graph, Discrete Math. 2 (1972), 179-181.C. H. C. Little. The parity of the number of 1-factors of a graph. Discrete Mathematics 2 (1972), 179-181....
Determining the winner of a Parity Game is a major problem in computational complexity with a number of applications in verification. In a parameterized complexity setting, the problem has often been considered with parameters such as (directed versions
we present a lower bound by showing that precise interval analysis is at least as hard as computing the sets of winning positions in parity games. Our lower-bound proof relies on an encoding of parity games into systems of particular integer equations. Moreover, we present a simplification of...
We also give an alternate proof of the resulting theorem without using Pfaffians.Charles H.C. LittleDiscrete MathematicsCharles H.C. Little, The parity of the number of 1-factors of a graph, Discrete Math. 2 (1972), 179-181.C. H. C. Little. The parity of the number of 1-factors ...