List colouring of graphs and generalized Dyck paths
نویسندگان
چکیده
منابع مشابه
On 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].
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The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...
متن کاملGame List Colouring of Graphs
We consider the two-player game defined as follows. Let (G,L) be a graph G with a list assignment L on its vertices. The two players, Alice and Bob, play alternately on G, Alice having the first move. Alice’s goal is to provide an L-colouring of G and Bob’s goal is to prevent her from doing so. A move consists in choosing an uncoloured vertex v and assigning it a colour from the set L(v). Adjac...
متن کاملList backbone colouring of graphs
Suppose G is a graph and H is a subgraph of G. Let L be a mapping that assigns to each vertex v of G a set L(v) of positive integers. We say (G,H) is backbone L-colourable if there is a proper vertex colouring c of G such that c(v) ∈ L(v) for all v ∈ V , and |c(u) − c(v)| > 2 for every edge uv in H . We say (G,H) is backbone k-choosable if (G,H) is backbone Lcolourable for any list assignment L...
متن کامل3-List Colouring Permutation Graphs
3-list colouring is an NP-complete decision problem. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list colouring on permutation graphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.11.022