TY - JOUR
T1 - Partitions of a graph into paths with prescribed endvertices and lengths
AU - Enomoto, Hikoe
AU - Ota, Katsuhiro
PY - 2000/6
Y1 - 2000/6
N2 - For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σki=1 ai and σ2(G) ≥ n+k - 1, then for any k vertices v1, v2, . . . , vk in G, there exist vertex-disjoint paths P1, P2, . . ., Pk such that | V(Pi)| = ai and vi is an endvertex of Pi for 1 ≤i≤ k. In this paper, we verify the conjecture for the cases where almost all ai≤5, and the cases where k≤3.
AB - For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σki=1 ai and σ2(G) ≥ n+k - 1, then for any k vertices v1, v2, . . . , vk in G, there exist vertex-disjoint paths P1, P2, . . ., Pk such that | V(Pi)| = ai and vi is an endvertex of Pi for 1 ≤i≤ k. In this paper, we verify the conjecture for the cases where almost all ai≤5, and the cases where k≤3.
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U2 - 10.1002/1097-0118(200006)34:2<163::AID-JGT5>3.0.CO;2-K
DO - 10.1002/1097-0118(200006)34:2<163::AID-JGT5>3.0.CO;2-K
M3 - Article
AN - SCOPUS:0034197810
VL - 34
SP - 163
EP - 169
JO - Journal of Graph Theory
JF - Journal of Graph Theory
SN - 0364-9024
IS - 2
ER -