TY - JOUR
T1 - Packing d-degenerate graphs
AU - Bollobás, Béla
AU - Kostochka, Alexandr
AU - Nakprasit, Kittikorn
N1 - Funding Information:
E-mail addresses: [email protected] (B. Bollobás), [email protected] (A. Kostochka), [email protected] (K. Nakprasit). 1 Research supported by NSF grants CCR-0225610 and DMS-0505550. 2 Research supported by the NSF grants DMS-0099608 and DMS-0400498.
PY - 2008/1
Y1 - 2008/1
N2 - We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobás-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d, Δ1, Δ2 ≥ 1 and n > max {40 Δ1 ln Δ2, 40 d Δ2} then a d-degenerate graph of maximal degree Δ1 and a graph of order n and maximal degree Δ2 pack. We use this result to show that, for d fixed and n large enough, one can pack frac(n, 1500 d2) arbitrary d-degenerate n-vertex graphs of maximal degree at most frac(n, 1000 d ln n).
AB - We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobás-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d, Δ1, Δ2 ≥ 1 and n > max {40 Δ1 ln Δ2, 40 d Δ2} then a d-degenerate graph of maximal degree Δ1 and a graph of order n and maximal degree Δ2 pack. We use this result to show that, for d fixed and n large enough, one can pack frac(n, 1500 d2) arbitrary d-degenerate n-vertex graphs of maximal degree at most frac(n, 1000 d ln n).
KW - Graph packing
KW - Maximum degree
KW - d-Degenerate graphs
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U2 - 10.1016/j.jctb.2007.05.002
DO - 10.1016/j.jctb.2007.05.002
M3 - Article
AN - SCOPUS:36048963352
SN - 0095-8956
VL - 98
SP - 85
EP - 94
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
IS - 1
ER -