TY - JOUR

T1 - Graph decompositions and D3-paths with a prescribed endvertex

AU - Enomoto, Hikoe

AU - Matsunaga, Shinsuke

AU - Katsuhiro, Ota

N1 - Funding Information:
E-mail address: shonan@media.teu.ac.jp (S. Matsunaga) 1Partially supported by JSPS Research Fellowships for Young Scientists.

PY - 2000/2/28

Y1 - 2000/2/28

N2 - Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑ki=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

AB - Let k and n be positive integers. Let G be a graph of order n≤4k, and let n = ∑ki=1 ai be a partition of n into k positive integers ai with 1≤ai≤4. In Matsunaga (Preprint, 1995) one of the authors proved that if G is 2-connected and the minimum degree of G is at least k, then with certain types of exceptions being allowed, the vertex set of G can be decomposed into k disjoint subsets Al,...,Ak so that |Ai| = ai and "the subgraph induced by Ai is connected" for all i, 1≤i≤k. In the present paper we extend this result for connected graphs in general. The paper also features the existence of D3-paths with a prescribed endvertex in a graph. (A D3-path in a graph is a path of the graph whose removal leaves no component of order at least 3.)

KW - D-path

KW - Graph decomposition

UR - http://www.scopus.com/inward/record.url?scp=0043284116&partnerID=8YFLogxK

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U2 - 10.1016/S0012-365X(99)00170-3

DO - 10.1016/S0012-365X(99)00170-3

M3 - Conference article

AN - SCOPUS:0043284116

VL - 213

SP - 87

EP - 104

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

T2 - Selected Topics in Discrete Mathematics

Y2 - 26 August 1996 through 28 September 1996

ER -