On the number of edge-disjoint one factors and the existence of k-factors in complete multipartite graphs
نویسندگان
چکیده
In this paper we use Tutte's f-factor theorem and the method of amalgamations to find necessary and sufficient conditions for the existence of a k-factor in the complete multipartite graph K(p(1 ) ..... p(n)), conditions that are reminiscent of the Erd6s-Gallai conditions for the existence of simple graphs with a given degree sequence. We then use this result to investigate the maximum number of edge-disjoint 1-factors in K ( p ( l ) . . . . . p(n)), settling the problem in the case where this number is greater than 6 p(2), where p(1 ) ~< p(2) ~ • • • ~< p(n).
منابع مشابه
On the signed Roman edge k-domination in graphs
Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...
متن کاملEdge-disjoint Decompositions of Complete Multipartite Graphs into Gregarious Long Cycles
The notion of gregarious cycles in complete multipartite graphs was introduced by Billington and Hoffman in 2003 and was modified later by Billington, Hoffman, and Rodger and by Billington, Smith, and Hoffman. In this paper, we propose a new definition of gregarious cycles in complete multipartite graphs which generalizes all of the three definitions. With our definition, we can consider gregar...
متن کاملDistinct edge geodetic decomposition in graphs
Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملLiftings in Finite Graphs and Linkages in Infinite Graphs with Prescribed Edge-Connectivity
Let G be a graph and let s be a vertex of G. We consider the structure of the set of all lifts of two edges incident with s that preserve edge-connectivity. Mader proved that two mild hypotheses imply there is at least one pair that lifts, while Frank showed (with the same hypotheses) that there are at least (deg(s) − 1)/2 disjoint pairs that lift. We consider the lifting graph: its vertices ar...
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 Mathematics
دوره 160 شماره
صفحات -
تاریخ انتشار 1996