Packing trees into n-chromatic graphs
نویسنده
چکیده
We show that if a sequence of trees T1, T2, ..., Tn−1 can be packed into Kn then they can be also packed into any n-chromatic graph.
منابع مشابه
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths. Several lower and upper bounds are obtained for the packing chromatic number of Cartesian products of graphs. It is proved that the packing chromatic number of the infinite hexagonal lattice lies between 6 and 8. Optimal lower a...
متن کاملGeneralizations of the tree packing conjecture
The Gyárfás tree packing conjecture asserts that any set of trees with 2, 3, . . . , k vertices has an (edge-disjoint) packing into the complete graph on k vertices. Gyárfás and Lehel proved that the conjecture holds in some special cases. We address the problem of packing trees into k-chromatic graphs. In particular, we prove that if all but three of the trees are stars then they have a packin...
متن کاملOn packing chromatic number of subcubic outerplanar graphs
The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the weak ...
متن کاملSubdivision into i-packings and S-packing chromatic number of some lattices
An i-packing in a graph G is a set of vertices at pairwise distance greater than i. For a nondecreasing sequence of integers S = (s1, s2, . . .), the S-packing chromatic number of a graph G is the least integer k such that there exists a coloring of G into k colors where each set of vertices colored i, i = 1, . . . , k, is an si-packing. This paper describes various subdivisions of an i-packing...
متن کاملJust chromatic exellence in fuzzy graphs
A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 34 شماره
صفحات -
تاریخ انتشار 2014