# Discrete Mathematics

Discrete Mathematics > 1998 > 189 > 1-3 > 43-68

^{n}

^{-}

^{1}x

^{n}

^{-}

^{1}

_{i}

_{=}

_{1}t

_{i}(1 - x)

^{i}, where t

_{i}is the number of spanning trees with external activity 0 and internal activity i. Moreover, it is known (via commutative...

Discrete Mathematics > 1999 > 199 > 1-3 > 227-231

Discrete Mathematics > 1999 > 202 > 1-3 > 239-248

Discrete Mathematics > 1999 > 203 > 1-3 > 71-82

_{r}(G)=P(G,r)/r!. Thus χ(G)=r and s

_{r}(G)=1 iff G is uniquely r-colourable. It is known that if G is uniquely 3-colourable, then e(G)>=2v(G)-3. In this paper, we show that if G is a 3-colourable connected graph with e(G)=2v(G)-k where k>=4, then s

_{3}(G)>=2

^{k}

^{-}

^{3}; and if, further, G is 2-connected and s...

Discrete Mathematics > 2000 > 224 > 1-3 > 107-124

_{p,q}by deleting a set of s edges. In this paper, we prove that for any graph G∈K2−s(p,q) with p⩾q⩾3 and 1⩽s⩽q−1, if the number of 3-independent partitions of G is at most 2

^{p−1}+2

^{q−1}+s+2, then G is χ-unique. It follows that any graph in K2−s(p,q)...

Discrete Mathematics > 2001 > 226 > 1-3 > 387-396

Discrete Mathematics > 2001 > 232 > 1-3 > 119-130

Discrete Mathematics > 2002 > 242 > 1-3 > 17-30

Discrete Mathematics > 2002 > 243 > 1-3 > 217-221

Discrete Mathematics > 2002 > 247 > 1-3 > 201-213

_{e}that has only the vertices u and w in common with the rest of G. Two mutually dual formulas are proved for the Tutte polynomial of G in terms of parameters of the graphs H

_{e}and (in the one case) flow polynomials of subgraphs of G or (in the other case) tension...

Discrete Mathematics > 2002 > 250 > 1-3 > 281-289

Discrete Mathematics > 2002 > 258 > 1-3 > 303-321

_{i}...

Discrete Mathematics > 2002 > 258 > 1-3 > 161-177

_{4}-homeomorphs which has exactly 2 adjacent paths of length 1, and give sufficient and necessary condition for the graphs in the family to be chromatically unique.

Discrete Mathematics > 2002 > 259 > 1-3 > 369-381

Discrete Mathematics > 2002 > 259 > 1-3 > 37-57

Discrete Mathematics > 2004 > 275 > 1-3 > 385-390

Discrete Mathematics > 2004 > 275 > 1-3 > 311-317

Discrete Mathematics > 2004 > 278 > 1-3 > 209-218

Discrete Mathematics > 2004 > 282 > 1-3 > 95-101

_{n}denote the set of simple graphs of order n. For any graph G in G

_{n}, let P(G,λ) denote its chromatic polynomial. In this paper, we first show that if G G

_{n}and χ(G)=<n-3, then P(G,λ) is zero-free in the interval (n-4+β/6-2/β,+~), where β=(108+1293)

^{1}

^{/}

^{3}and β/6-2/β (=0.682327804...) is the only real root of x

^{3}...

Discrete Mathematics > 2004 > 282 > 1-3 > 103-112

^{1}

^{/}

^{3}, and n-1+(n-3)(n-7)/2,...