There was no AP Poll in 1935; official selection of National Champions began in 1936. (There was an AP Poll in 1934.)
IN 1919 A&M was selected along with Harvard, Illinois and Notre Dame. A&M was selected by the Nat'l Champoinship Foundation (NCF), Harvard was selected by the NCF, the College FB Research Assn.(CFRA)and the Helms Athletic Foundation(HAF) Ill. was selected by the CFRA. Notre Dame was selected by the NCF.
Texas A&M was selected again in 1935 by the AP.
In 1919 they went undefeated and unscored upon, but were not the only team to claim the national title.
In 1939 they went undefeated and were named national champions by the national championship foundation.
Yes, they played in the 2006 BCS National Championship
The Maine Bears have never won a National Championship in football.
They have won 11 national football championships