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CHARACTERIZATION THEOREMS FOR CERTAIN CLASSES OF INFINITE GRAPHS
정환옥 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.1
In this paper we present a necessary and sufficient conditions for an infinite VAP-free plane graph to be a 3LV-graph as well as an LV-graph. We also introduce and investigate the concept of the order and the kernel of an infinite connected graph containing no one-way infinite path.
EXISTENCE OF SPANNING 3-TREES IN A 3-CONNECTED LOCALLY FINITE VAP-FREE PLANE GRAPH
정환옥 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper we prove the existence of spanning 3-trees in a 3-connected infinite locally finite VAP-free plane graph. Together with the results of Barnette and the author, this yields that every finite or infinite 3-connected locally finite VAP-free plane graph contains a spanning 3-tree.
Existence of spanning 4-subgraphs of an infinite strong triangulation
정환옥 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph with maximum degree 4 in such a graph
Plane embedding problems and a theorem for infinitemaximal planar graphs
정환옥 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced -path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new -path is constructed such that the resulting fan is tight.
Spanning 3-forests in bridges of a tight semiring in an LV-graph
정환옥 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
An infinite locally finite plane graph is an LV-graph if it is 3-connected and VAP-free. In this paper, as a preparatory work for solving the problem concerning the existence of a spanning 3-tree in an LV-graph, we investigate the existence of a spanning 3-forest in a bridge of type 0,1 or 2 of a tight semiring in an LV-graph satisfying certain conditions. An infinite locally finite plane graph is an LV-graph if it is 3-connected and VAP-free. In this paper, as a preparatory work for solving the problem concerning the existence of a spanning 3-tree in an LV-graph, we investigate the existence of a spanning 3-forest in a bridge of type 0,1 or 2 of a tight semiring in an LV-graph satisfying certain conditions.
Some problems and results on circuit graphs and triangular graphs
정환옥 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.
Hamiltonicity of Locally 2-connected Claw-free Graphs
정환옥 한신대학교 1998 한신논문집 Vol.15 No.1
In this paper we show that every connected, locally 2-connected graph containing no induced subgraph isomorphic to K₁, ₃is hamiltonian-connected, which improves the result of Chartrand and et al.
A structure theorem and a classification of an infinite locally finite planar graph
정환옥 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness. In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.