• The Mathematical Education
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• v.16 no.2
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• pp.29-31
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• 1978

bipartite graph와 Euler graph의 정의를 사용하는 대신 이들 graph가 나타내는 특성을 사용하여 bipartite matroid와 Euler matroid를 정의하고 이들 matroid가 binary일 때 서로 dual 의 관계가 있음을 증명한다. 이 관계를 이용하여 bipartite graph와 Euler graph의 성질을 밝힐수 있다.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.3
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• pp.119-124
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• 2014

Let G = (V, E) be a graph. Maximum Bipartite Subgraph Problem is to convert a graph G into a bipartite graph by removing minimum number of edges. This problem belongs to NP-complete; hence, in this research, we are suggesting a new metaheuristic algorithm which combines Tabu search and GRASP.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.331-335
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• 2008

In this paper, we investigate the number of ones in rows of Pascal's Rectangle. Using these results, we determine the existence of regular bipartite Steinhaus graphs. Also, we give an upper bound for the minimum degree of bipartite Steinhaus graphs.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.215-224
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• 2006

We call the bipartite graph G is normal provided the reduced adjacency matrix A of G is normal. In this paper we give graph representations of normal matrices. In addition we shall have the characterization of signed bipartite normal graphs.

• The KIPS Transactions:PartD
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• v.15D no.1
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• pp.15-22
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• 2008

In this paper, we propose an efficient algorithm using only one-time database scan. The proposed algorithm creates the bipartite graph which indicates relationship of large items and transactions including the large items. And then we can find large itemsets using the bipartite graph. The bipartite graph is generated when database is scanned to find large items. We can't easily find transactions which include large items in the large database. In the bipartite graph, large items and transactions are linked each other. So, we can trace the transactions which include large items through the link information. Therefore the bipartite graph is a indexed database which indicates inclusion relationship of large items and transactions. We can fast find large itemsets because proposed method conducts only one-time database scan and scans indexed the bipartite graph. Also, it don't generate candidate itemsets.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.25-37
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• 2019

Let G be a bipartite graph with (X, Y ) as its bipartition. Let B be a complete bipartite graph with a bipartition ($V_1$, $V_2$) such that $X{\subseteq}V_1$ and $Y{\subseteq}V_2$. A bi-packing of G in B is an injection ${\sigma}:V(G){\rightarrow}V(B)$ such that ${\sigma}(X){\subseteq}V_1$, ${\sigma}(Y){\subseteq}V_2$ and $E(G){\cap}E({\sigma}(G))={\emptyset}$. In this paper, we show that if G is a bipartite graph of order n with girth at least 12, then there is a complete bipartite graph B of order n + 1 such that there is a bi-packing of G in B. We conjecture that the same conclusion holds if the girth of G is at least 8.

• East Asian mathematical journal
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• v.25 no.2
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• pp.215-220
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• 2009

In this paper, we investigate the generating strings and the number of 2-(edge)connected bipartite Steinhaus graphs.

• East Asian mathematical journal
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• v.26 no.3
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• pp.423-427
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• 2010

In this paper, we give an upper bound for dominations of Steinhaus graphs, and the domination numbers of the bipartite Steinhaus graphs. Also, we give an upper bound for Nordhaus-Gaddum type result for the bipartite Steinhaus graphs.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.403-414
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• 2012

A voltage assignment on a graph was used to enumerate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph $K_{m,n}$ is surprisingly the ($m,n$) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph $K_{m,n}$ for which voltage assignments are either -1 or 1 and that every link is the boundary of a complete bipartite graph $K_{2,n}$ for which voltage assignments are either -1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.