Vizing's conjecture: A two-thirds bound for claw-free graphs
نویسنده
چکیده
منابع مشابه
Vizing's conjecture: a survey and recent results
Vizing’s conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this paper we survey the approaches to this central conjecture from domination theory and give some new results along the way. For instance, several new properties of a minimal counterexample to the conjecture are obtained an...
متن کاملOn a conjecture on total domination in claw-free cubic graphs: proof and new upper bound
In 2008, Favaron and Henning proved that if G is a connected claw-free cubic graph of order n ≥ 10, then the total domination number γt(G) of G is at most 5 11 n, and they conjectured that in fact γt(G) is at most 4 9 n (see [O. Favaron and M.A. Henning, Discrete Math. 308 (2008), 3491–3507] and [M.A. Henning, Discrete Math. 309 (2009), 32–63]). In this paper, in a first step, we prove this con...
متن کاملOn the Erdös-Gyárfás conjecture in claw-free graphs
The Erdős-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erdős-Gyárfás conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free graphs.
متن کاملTotal coloring for generalized Sierpinski graphs
A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the generalized Sierpiński graphs of cycle graphs and hypercube graphs. We give a total coloring for the WK-recursive topology, whi...
متن کاملAn approximate version of Hadwiger's conjecture for claw-free graphs
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class of claw-free graphs (graphs that do not have a vertex with three pairwise nonadjacent neighbors). Our main result is that a claw-free graph with chromatic number χ has a clique minor of size ⌈23χ⌉.
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:
- Discrete Applied Mathematics
دوره 230 شماره
صفحات -
تاریخ انتشار 2017