[PDF] Top 20 Packing complete multipartite graphs with 4-cycles

... of 4-cycles in a maximum packing of the complete bipartite graph V 2iÿ1 0 [ V 2i 0 , chosen so that the leave G 0 i satis®es G 0 i  G i ; this is possible since jV j j  jV j 0 j (mod ... See full document

... vertex-disjoint graphs, then G _ H is formed from the union of G and H by joining each vertex in G to each vertex in H with exactly one ...k-cycle packing C as an ordered pair ðV ; CÞ, where V is the ... See full document

... a complete m-partite graph with partite sets of sizes n 1 , n 2 , ...A complete m-partite graph is balanced if each partite set has n ver- ...this complete m-partite graph by K m(n) ...maximum ... See full document

... rectangles with disjoint projections in the same direction thus these cannot represent C 4 ...representation with two rectangles per vertex for G ...G with the vertices grouped by partite ... See full document

... Now, let P be the subgraph of H induced by all edges with positive weight, and let Q be the subgraph of H induced by all edges with nonposi- tive weight. Replace each negative edge-weight in Q by its ... See full document

... (ii) B s−1 ¿ A s−1 . First, if s−1¿3, then rearrange V 1 ; V 2 ; : : : ; V k to the order V 1 ; V 2 ; : : : ; V s−2 , V s ; V s+1 ; : : : ; V k ; V s−1 . Now, the proof can be obtained by a similar idea as that of Case ... See full document

... A packing of a graph T with triangles is a partition of the edge set of a subgraph G of T , each element of which induces a triangle; the remainder graph of this packing, also known as the leave, is ... See full document

... n with the property that any integer occurs once in each row and ...the complete graph with vertex set { 0 , 1 , 2 , 3 , 4 } and let C 1 = h 0 , 1 , 2 , 3 , 4 , 0 i , C 2 = h 0 , 2 , 3 ... See full document

... As another example, a Latin square of order n is an n × n array containing the integers from 1 to n, arranged so that each integer appears exactly once in each row, and exactly once in each column. If we delete some rows ... See full document

... Abstract The path-partition problem is to find a minimum number of vertex-disjoint paths that cover all vertices of a given graph. This paper studies the path-partition problem from an algorithmic point of view. As the ... See full document

... In this paper, we find an upper bound for the achromatic index of the regular complete multipartite graph which forces the inequality to be an equality and a c[r] ... See full document

... Keywords: Hypercubes; Embedding; Hamiltonian cycles; Incrementally Extensible Hypercubes; Interconnection networks.. Introduction.[r] ... See full document

... − n=2 for even n). Then K n (respectively, K n − F) can be decomposed into cycles C 1 ; C 2 ; : : : ; C h such that the length of C i is m i for i = 1; 2; : : : ; h. In this paper, we prove a special case of the ... See full document

... Cayley graphs, is one of the most versatile interconnection networks for parallel and distributed ...incident with two or more fault-free edges, we show that an n-dimensional alternating group graph can ... See full document

... Each application of Step 3 in Algorithm 2.1 will produce at least one more one in the uncrossed entries in the matrix and leave all the ones unchanged, unless they are crossed by [r] ... See full document

... Hence, there exists a ( σ 1 ( G) − 1)-edge coloring of H − M 1 . Notice that |E(H − M 1 ) | = (σ 1 ( G) − 1)m. But then there exists an equalized (σ 1 ( G) − 1)-edge color- ing of H − M 1 , so that each color class has ... See full document

... In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split grap[r] ... See full document

... r-dimensional k-ary butterfly graph with 2k - 2 edge faults contains a Hamiltonian cycle. However, the proof seems very hard[r] ... See full document

... Keywords: Intersection graph; Interval number; Total interval graph; Complete r-partite graph 1. Introduction The intersection graph of a family F of sets is the graph obtained by representing each set of F as a ... See full document

... i Department of Information Engineering, Feng Chia University, Taichung 40724, Taiwan 2 Institute of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan.. An e[r] ... See full document