A one-to-one correspondence between potential solutions of the cluster deletion problem and the minimum sum coloring problem, and its application to {k}-sparse graphs
نویسندگان
چکیده
In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in G (i.e. the complement graph of G). We apply this correspondence to polynomially solve the cluster deletion problem in a subclass of P4-sparse graphs that strictly includes P4-reducible graphs.
منابع مشابه
A one - to - one correspondence between potential solutions of the cluster deletion problem and the minimum sum coloring problem , and its application to P 4 - sparse graphs ∗
In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in G (i.e. the complement graph of G). We apply this correspondence to polynomially solve the cluster deletion problem in a subclass of P4-sparse graphs that strictly includes P4-reducible graphs.
متن کاملOn the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
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 کاملEnumeration of Dominant Solutions: An Application in Transport Network Design
A One-Dimensional Binary Integer Programming Problem (1DB-IPP) is concerned with selecting a subset from a set of k items in budget constraint to optimize an objective function. In this problem a dominant solution is defined as a feasible selection to which no further item could be added in budget constraint. This paper presents a simple algorithm for Enumeration of Dominant Solutions (EDS) and...
متن کاملThe Extent of Correspondence between the Content of the 9th Grade Math Textbook and the Real World Issues
Education has always been one of the main concerns of human societies, but in different periods and different communities educational goals have varied. Nowadays, and especially here in Iran, the main goal of education is to prepare children for real life and its problem. More specifically, the goal in mathematics education is help students with solving real life problems using their acquired m...
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:
- Inf. Process. Lett.
دوره 115 شماره
صفحات -
تاریخ انتشار 2015