# Discrete Mathematics

Discrete Mathematics > 1998 > 187 > 1-3 > 233-244

_{1,3}. Let k be a positive integer. Our main result is as follows: If G is a claw-free graph of order at least 3k and d(x) + d(y)⩾3k + 1 for every pair of non-adjacent vertices x and y of G, then G contains k vertex-disjoint triangles unless either k is odd and G is one exceptional graph of order 3k +...

Discrete Mathematics > 2001 > 230 > 1-3 > 113-118

_{1,4}-free graph G with minimum degree δ(G)⩾k+3 is pancyclic modk and every claw-free graph G with δ(G)⩾k+1 is pancyclic modk, which confirms Thomassen's conjecture (J. Graph Theory 7 (1983) 261–271) for claw-free graphs.

Discrete Mathematics > 2001 > 231 > 1-3 > 191-197

Discrete Mathematics > 2002 > 243 > 1-3 > 195-200

_{1,3}. We prove that if G is a claw-free graph with minimum degree at least d, then G has a path factor such that the order of each path is at least d+1.

Discrete Mathematics > 2002 > 256 > 1-2 > 151-160

_{1,3}-free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K

_{1,3}-free graph with a minimum degree sum δ2>2 3n+1−4; every {K

_{1,3},P

_{7}}-free graph with δ

_{2}⩾9; every {K

_{1,3},Z

_{4}}-free graph with δ

_{2}⩾9; and every K

_{1,3}-free graph with maximum...

Discrete Mathematics > 2003 > 272 > 1 > 107-118

_{n}be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for H

_{n}. Here we determine the asymptotic behavior of this sequence:H

_{n}~(2n)!e6πnn2e

^{n}

^{/}

^{3}e

^{(}

^{n}

^{/}

^{2}

^{)}

^{1}

^{/}

^{3}.We have verified this formula using known asymptotic...

Discrete Mathematics > 2004 > 277 > 1-3 > 1-13

Discrete Mathematics > 2005 > 294 > 3 > 303-309

Discrete Mathematics > 2006 > 306 > 15 > 1812-1816

Discrete Mathematics > 2006 > 306 > 22 > 2983-2988

Discrete Mathematics > 2007 > 307 > 11-12 > 1266-1275

Discrete Mathematics > 2008 > 308 > 7 > 1260-1267

Discrete Mathematics > 2008 > 308 > 9 > 1612-1619

Discrete Mathematics > 2008 > 308 > 9 > 1628-1633

Discrete Mathematics > 2008 > 308 > 24 > 6558-6563

Discrete Mathematics > 2010 > 310 > 10-11 > 1564-1572

Discrete Mathematics > 2011 > 311 > 21 > 2475-2484

Discrete Mathematics > 2012 > 312 > 14 > 2177-2189

Discrete Mathematics > 2012 > 312 > 21 > 3107-3116

Discrete Mathematics > 2013 > 313 > 4 > 460-467