The chromatic index of graphs of high maximum degree
نویسندگان
چکیده
منابع مشابه
The chromatic index of graphs with large maximum degree
By Vizing’s theorem, the chromatic index x’(G) of a simple graph G satisfies d(G) Li 1 V(G)1 J + ir, where r is the number of vertices of maximum degree. A graph G is critical if G is Class 2 and x’(H) < x’(G) for all prop...
متن کاملChromatic index, treewidth and maximum degree
We conjecture that any graphG with treewidth k and maximum degree ∆(G) ≥ k + √ k satisfies χ′(G) = ∆(G). In support of the conjecture we prove its fractional version.
متن کاملThe Game Chromatic Index of Forests of Maximum Degree 5
Using a refinement of the methods of Erdös et al. [6] we prove that the game chromatic index of forests of maximum node degree 5 is at most 6. This improves the previously known upper bound 7 for this parameter. The bound 6 is tight [6].
متن کاملOn the chromatic index of graphs whose core has maximum degree two
Let G be a connected graph. The core of G, denoted by G∆, is the subgraph of G induced by the vertices of maximum degree. Hilton and Zhao [On the edge-colouring of graphs whose core has maximum degree two, JCMCC 21 (1996), 97-108] conjectured that, if ∆(G∆) ≤ 2, then G is Class 2 if and only if G is overfull, with the sole exception of the Petersen graph with one vertex deleted. In this paper w...
متن کاملThe Total Chromatic Number of Graphs of High Minimum Degree
If G is a simple graph with minimum degree <5(G) satisfying <5(G) ^ f(| K(C?)| -f-1) the total chromatic number conjecture holds; moreover if S(G) ^ f| V(G)\ then #T(G) < A(G) + 3. Also if G has odd order and is regular with d{G) ^ \^/1\V{G)\ then a necessary and sufficient condition for ^T((7) = A((7)+ 1 is given.
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: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00306-h