Minmax relations for cyclically ordered digraphs
نویسندگان
چکیده
منابع مشابه
Minmax relations for cyclically ordered digraphs
We prove a range of minmax theorems about cycle packing and covering in digraphs whose vertices are cyclically ordered, a notion promoted by Bessy and Thomassé in their beautiful proof of the following conjecture of Gallai: the vertices of a strongly connected digraph can be covered by at most as many cycles as the stability number. The results presented here provide relations between cycle pac...
متن کاملCyclically k-partite digraphs and k-kernels
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent set of vertices (if u, v ∈ N then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l). A k-kernel is a (k, k − 1)-kernel. A digraph D is cyclically k-partite if there exists a partition {Vi} i=0 of V (D) suc...
متن کاملPattern avoidance in cyclically ordered structures
We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the first one corresponding to classical permutation avoidance. The cyclic modification allows for circular shifts in the entries. Using two bijections, both ascribable to both Deutsch and Krattenthaler independently, we sin...
متن کاملFormal power series with cyclically ordered exponents
We define and study a notion of ring of formal power series with exponents in a cyclically ordered group. Such a ring is a quotient of various subrings of classical formal power series rings. It carries a two variable valuation function. In the particular case where the cyclically ordered group is actually totally ordered, our notion of formal power series is equivalent to the classical one in ...
متن کاملLinkedness and Ordered Cycles in Digraphs
Given a digraph D, let δ(D) := min{δ(D), δ−(D)} be the minimum degree of D. We show that every sufficiently large digraph D with δ(D) ≥ n/2 + l − 1 is l-linked. The bound on the minimum degree is best possible and confirms a conjecture of Manoussakis [16]. We also determine the smallest minimum degree which ensures that a sufficiently large digraph D is k-ordered, i.e. that for every sequence s...
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: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.09.005