Minimally Unbalanced Diamond-Free Graphs and Dyck-Paths
نویسندگان
چکیده
منابع مشابه
Minimally unbalanced diamond-free graphs and Dyck-paths
A {0, 1}-matrix A is balanced if it does not contain a submatrix of odd order having exactly two 1’s per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrarily to what happened for perfect graphs. In this paper, we provide such a chara...
متن کاملPairs of noncrossing free Dyck paths and noncrossing partitions
Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n + 1] with n + 1 blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.
متن کاملDyck paths , Motzkin paths and traffic jams
It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the asymmetric exclusion process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee–Yang theory of partition function zeros to ...
متن کاملColouring Diamond-free Graphs
The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we classify the computational complexity of Colouring for (diamond, H)-free graphs. Our proof is based on combining known results together with proving that the clique-width is bounded for (diamond, P1+2P2)-free graphs. Our technique for han...
متن کاملOn Generalized Dyck Paths
We generalize the elegant bijective proof of the Chung Feller theorem from the paper of Young-Ming Chen [The Chung-Feller theorem revisited, Disc. Math. 308 (2008), 1328–1329].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140981496