The total chromatic number of any multigraph with maximum degree five is at most seven

نویسنده

  • Alexandr V. Kostochka
چکیده

The result announced in the title is proved. A new proof of the total 6-colorability of any multigraph with maximum degree 4 is also given.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The distinguishing chromatic number of bipartite graphs of girth at least six

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling   with $d$ labels  that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...

متن کامل

An asymptotically tight bound on the adaptable chromatic number

The adaptable chromatic number of a multigraph G, denoted χa(G), is the smallest integer k such that every edge labeling of G from [k] = {1, 2, · · · , k} permits a vertex coloring of G from [k] such that no edge e = uv has c(e) = c(u) = c(v). Hell and Zhu proved that for any multigraph G with maximum degree ∆, the adaptable chromatic number is at most lp e(2∆− 1) m . We strengthen this to the ...

متن کامل

List total colorings of graphs

We introduce the concept of list total colorings and prove that every multigraph of maximum degree 3 is 5-total-choosable. We also show that the total-choosability of a graph of maximum degree 2 is equal to its total chromatic number.

متن کامل

The chromatic index of multigraphs of order at most 10

The maximum of the maximum degree and the 'odd set quotients' provides a well-known lower bound 4)(G) for the chromatic index of a multigraph G. Plantholt proved that if G is a multigraph of order at most 8, its chromatic index equals qS(G) and that if G is a multigraph of order 10, the chromatic index of G cannot exceed qS(G) + 1. We identify those multigraphs G of order 9 and 10 whose chromat...

متن کامل

Irregular embeddings of multigraphs with fixed chromatic number

Let G be a c-chromatic multigraph (c >t 2) with maximum edge multiplicity s. In this note we show that G has an embedding as an induced subgraph, into some degree irregular c-chromatic multigraph having the same maximum edge multiplicity.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 162  شماره 

صفحات  -

تاریخ انتشار 1996