The trail number of a graph


The trail number of tr (G) of a graph G is the maximum length of a trail in it. Consider the set of all connected graphs with n vertices and m edges. We first easily determine the exact maximum value of tr (G) among these graphs. Then we give the exact minimum provided m ≤ 4 (n-1)/3. Finally we prove an asymptotically correct estimate of the minimum of tr (G) for all values of n and m. © 1982, North-Holland Publishing Company

Publication Title

North-Holland Mathematics Studies