Lower bounds for the greatest possible number of colors in interval edge colorings of bipartite cylinders and bipartite tori
نویسندگان
چکیده
An interval edge t − coloring of a graph G is a proper edge coloring of G with colors 1, 2, , t ... such that at least one edge of G is colored by color , 1, 2, , i i t = ... , and the edges incident with each vertex ( ) v V G ∈ are colored by ( ) G d v consecutive colors, where ( ) G d v is the degree of the vertex v in G . In this paper interval edge colorings of bipartite cylinders and bipartite tori are investigated.
منابع مشابه
Interval cyclic edge-colorings of graphs
A proper edge-coloring of a graph G with colors 1, , t is called an interval cyclic t coloring if all colors are used, and the edges incident to each vertex ( ) v V G are colored with ( ) G d v consecutive colors by modulo t , where ( ) G d v is the degree of the vertex v in G . In this paper some properties of interval cyclic edge-colorings are investigated. Also, we give some bounds for...
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملZarankiewicz Numbers and Bipartite Ramsey Numbers
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
متن کاملOn restricted edge-colorings of bicliques
We investigate the minimum and maximum number of colors in edge-colorings of Kn,n such that every copy of Kp,p receives at least q and at most q′ colors. Along the way we improve the bounds on some bipartite Turán numbers.
متن کاملSome results on interval edge colorings of (α, β)-biregular bipartite graphs
A bipartite graph G is called (α, β)-biregular if all vertices in one part of G have the degree α and all vertices in the other part have the degree β. An edge coloring of a graph G with colors 1, 2, 3, . . . , t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/0712.4148 شماره
صفحات -
تاریخ انتشار 2007