On vertex-disjoint complete subgraphs of a graph
نویسنده
چکیده
We conjecture that if G is a graph of order sk, where s ~3 and k 2: 1 are integers, and d(x)+d(y) ~ 2(s-1)k for every pair of non-adjacent vertices x and y of G, then G contains k vertex-disjoint complete subgraphs of order s. This is true when s = 3, [6]. Here we prove this conjecture for k ~ 6.
منابع مشابه
TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...
متن کاملVertex-disjoint subgraphs with high degree sums
For a graph G, we denote by σ2(G) the minimum degree sum of two non-adjacent vertices if G is non-complete; otherwise, σ2(G) = +∞. In this paper, we give the following two results; (i) If s1 and s2 are integers with s1, s2 ≥ 2 and if G is a non-complete graph with σ2(G) ≥ 2(s1 + s2 + 1) − 1, then G contains two vertexdisjoint subgraphs H1 and H2 such that each Hi is a graph of order at least si...
متن کاملCovering graphs by the minimum number of equivalence relations
An equivalence graph is a vertex disjoint union of complete graphs. For a graph G, let eq(G) be the irdnimum number of equivalence subgraphs of G needed to cover all edges of G. Similarly, let cc(G) be the minimum number of complete subgraphs of G needed to cover all its edges. Let H be a graph on n vertices with ma,'dmal degree _~d (and minimal degree --~ 1), and let G=I~ be its complement. We...
متن کاملOn Partitioning a Graph into Two Connected Subgraphs
Suppose a graph G is given with two vertex-disjoint sets of vertices Z1 and Z2. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z1 and Z2, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of n-vertex graphs G = (V, E) in which Z1 and Z2 each contai...
متن کاملSufficient Condition for the Existence of Three Disjoint Theta Graphs
A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order n ≥ 12 and size at least ⌊ 11n−18 2 ⌋ contains three disjoint theta graphs. As a corollary, every graph of order n ≥ 12 and size at least ⌊ 11n−18 2 ⌋ contains three disjoint cycles of even length. 1. Terminology and introduction In this paper, we only co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 16 شماره
صفحات -
تاریخ انتشار 1997