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suppose v 2k and consider a graph g consisting of two complete graphs one with k vertices x1xk and one with k 1
what is the minimum number of new bridges that would have to be built in kumlonigsberg and where could they be built in
if we built a new bridge in kumlonigsberg between the island and the top and bottom banks of the river could we take a
the hypercube graph qn has as its vertex set the n-tuples of zeros and ones two of these vertices are adjacent if and
we form the hamiltonian closure of a graph by constructing a sequence of graphs gi with g0 g and gi formed from gi-1
apply breadth-first search from vertex 0 in an alternating way to grapha in figure 626 does this method find an
table 62 shows a second sample of the kinds of applications a school district might get for its positions draw a graph
the k-path problem is the problem of determining whether a graph on n vertices has a path of length k where k is
the hamiltonian path problem is the problem of determining whether a graph has a hamiltonian path explain why this
a cut-vertex of a graph is a vertex whose removal along with all edges incident with it increases the number of
the complete bipartite graph kmn is a graph with m n vertices these vertices are divided into a set of size m and a
let g be a connected graph with no odd cycles let x beavertex of g let x be all vertices at an even distance from x and
what is the sum of the maximum size of an independent set and the minimum size of a vertex cover in a graph g hint it
consider the closed intervals 1 4 2 5 3 8 5 12 6 12 7 14 13 14 draw the interval graph determined by these intervals
a circuit is to be laid out on a computer chip in a single layer the design includes five terminals think of them as
as in the previous exercise we are laying out a computer circuit however we now have six terminals labeled a b c 1 2
draw some planar graphs with at least three faces and experiment to see if you can find a numerical relationship among
in theorem 617 is it true that if there is an augmenting path p with edge set ep for a matching m then mep is a larger
a star is a another name for a tree with one vertex connected to each of n other vertices so a star has n 1 vertices
let g consist of a five cycle and a complete graph on four vertices with all vertices of the five-cycle joined to all
the usual symbol for the maximum degree of any vertex in a graph is show that the chromatic number of a graph is no
a wheel on n vertices consists of a cycle on n - 1 vertices together with one more vertex normally drawn inside the
n a simple graph every face has at least three edges this means that the number of pairs of a face and an edge
a sawmill runs for three 4-hour shifts per day it produces 500 2x4s per hour which are divided into 50 piece bundles
the area of a given rectangular plate is a given value but its dimensions are not given one may make a cuboid without a